I have seen a lot of people ask what they should do if their Twin Flame arrives in their life when they are already engaged in a relationship with someone else. It's a heart-breaking situation for many folks and one I think I can help you with.
First, it is important that no matter how strong your feelings for your twin flame may be, they are only going to be in your life temporarily. Twin Flame connections are meant to be temporary. They're only meant to last as long as the two of you are working to heal the shared trauma energy you have between you. Keep this in mind as your libido and heart scream that maybe you should give up your primary partner in favor of having that intense relationship with your twin flame. Your primary partner, to whom you have made a commitment, it unlikely to take you back when your twin flame connection fades after the healing done. It is unfair to your primary partner to ask them to accept that what you did was "out of your control" or any such nonsense. You are in control of your own actions. That's really all you control in this world. If you choose to leave your primary partner for your twin flame, you're likely setting yourself up for heartache.
As for what to do when your twin flame comes into your life while you're engaged in a relationship with someone else, here are some tips on how to handle it.

Set Clear Boundaries
I'm an advocate of setting and holding to clear boundaries in any relationship, but with a twin flame, I'm even more so. As I mentioned, the emotional connection to a twin flame can be overwhelming. Suddenly you have this connection with someone who is so much like you, probably even more than your primary partner, that you can finish each other's sentences, and connect on the deepest levels. Because these feelings are so strong and feel so deep at the time you meet, you may allow yourself and your twin flame to explore them. If you love and cherish your primary partner, this is where you have to set clear boundaries. What are you willing to give up with your primary partner in order to explore the connection with your twin flame? How much are you willing to hurt your primary partner? Have you and your primary partner discussed what level of physical, emotional, and energetic intimacy is permitted between yourself and your twin flame? All of these questions will lead you to a boundary to maintain with your twin flame in order to not destroy your primary partnership.

And remember that these boundaries are in place to protect YOU, too. You know this is a temporary relationship. Are you willing to give up your integrity, honor, and love with your primary partner for something you know won't last? Knowing the answer to this question prior to engaging with your twin flame will make you life so much easier.

Set Clear Expectations
Do you expect your twin flame to be a part of your day-to-day life? Do you expect to be kept informed of any other emotional connections your twin flame engages in? Do you expect your twin flame to leave their primary partner for you? These are all important questions to ask yourself and then share with your twin flame.

It's okay to have whatever expectations you want to have, but you have to share them with your twin flame—and your primary partner—if you want to maintain healthy relationships with both partners. And understand that it is perfectly acceptable for either your twin flame or your primary partner to tell you that they cannot meet your expectation. You can only share what you expect, not demand that those expectations be met.

Hold to Your Boundaries
I know that in the moment, it can be difficult to stop your twin flame and say, "no, this is beyond my boundaries and I cannot do this." However, this is how you keep yourself and your primary partner sane. Sure, there might be a few moments when you consider breaking a boundary when your twin flame asks for more than you agreed to initially, but if you want your primary partnership to survive the twin flame connection, you have to be willing to tell your twin flame, "NO."

And that might be one of the hardest things you have to do in a situation like this. You and your twin flame often have nearly identical desires. When one of you says, "throw caution to the wind, let's do this," you may be sorely tempted to do so. But before you give in, ask yourself is the moment of pleasure in the twin flame connection worth losing what you have with your primary partner. If it is not, you must stand your ground, no matter how much your twin flame plays to your emotions and the shared trauma energy.

Remember that you and your twin flame are both damaged in some way, in the same way even. That kind of damage requires healing, not feeding. This person has come into your life to help you heal from that shared trauma, so if they ask you to break your boundaries, ask yourself why they're wanting to do that. It's likely part of what they came to you to help you heal. This is where you can start to see why healing the trauma is so important.
For example, you are trying to heal from having been cheated on and treated like an option in many past relationships, both in this life and others. When your twin flame says, "We can do this. We won't be hurting anyone. I love you, and I need this from you," what they're really doing is offering you the opportunity to be on the other side of the trauma you have suffered. To choose the path those in your own lives did not. To choose to be honorable and loving to your primary partner rather than to cheat (physically, emotionally, or energetically) with your twin flame. It's a teaching moment, but you have to be willing to tell them no to gain the benefit and healing from that moment.

Talk to Your Primary Partner
The most important thing to do when your twin flame comes into your life while you're in a relationship is to talk to your primary partner about what that means. Your partner is going to feel the connection between you and your twin flame unless they are a complete psychic null. That means, they're going to get insecure and wonder if you're going to leave them for the twin flame. It's up to you to clearly communicate your intentions—either to stay or go— and your expectations.

Talk to your primary partner about what it means to you to have your twin flame in your life. Talk about how much time you will want to spend with the twin flame. What kind of intimacy is allowed—and take your partner's feelings and desires into account here. Tell them everything that happens between you and your twin flame, in so much as your primary partner wants to know the details. Don't keep any secrets when it comes to your twin flame and your primary partner.

Look at the situation from the outside. If your partner's twin flame came into their life while they were involved with you, how would you feel? What would you want and need to know? Share all of these things with your primary partner and let them choose whether or not they are comfortable with the situation. You can ask them to stay, to be understanding, but you cannot make someone choose a path that will bring them pain.

Absolute transparency with your primary partner is really the only way your relationship with them can survive the arrival of a twin flame. They need to know you are being open and honest with them at all times—and you need to be open and honest with them at all times. You have to be willing to be reassuring to your primary partner when they feel lost and disconnected. You have to be willing to continue to invest yourself in your primary relationship, and demonstrate that willingness to your primary partner regularly if you want the relationship to survive.

Include Your Primary Partner
Allow you primary partner to be a part of your twin flame relationship whenever you can. This will help your primary partner find a level of comfort with your twin flame and help them to feel more secure in your relationship.
Including your primary partner in your twin flame connection also demonstrates to your twin flame that the boundaries you set, you meant. It will make sticking to your boundaries easier in the long run because then your primary partner is a person, not just an idea, to your twin flame. It's often much more difficult to hurt someone you know than it would be to hurt the idea of someone else in the world.

Listen to Your Primary Partner
There will be times when your primary partner is uncomfortable with your twin flame, no matter how well you prepare them for the situation. At these times, it is up to you to be understanding and willing to make changes to maintain the health of your primary relationship. It's all about priorities now.
Yes, healing your trauma is a priority. However, doing so at the expense of someone you love is likely not your focus. If your primary partner comes to you with a concern about your twin flame, listen. Don't react immediately, just listen. Hear what your partner is sharing. It is likely a fear of loss or rejection that they're sharing with you. When you hear your partner's concern and respond with love and compassion, the situation often dissipates more quickly than if you react and approach the situation with indignation and anger. Don't let your high emotions answer for you. Be calm and considerate and your primary partner will appreciate you more.

Twin flame connections are often volatile and burn out fast. Keep that in mind when you are deciding whether to stay in your primary relationship or leave in favor of your twin flame. Nine times out of ten, your twin flame connection is less than healthy. They're there to help you heal from trauma, but because they are also trying to heal from similar trauma, the two of you may trigger each other. That's why so many twin flame relationships blow up after a short time. Your primary partner shouldn't be a casualty of your twin flame connection. They deserve better than that from you. But only you can choose to be better for them. I hope these tips will help you better handle this kind of situation.

Oh, and that 10th time out of 10 when a twin flame relationship lasts? That's the unicorn situation where you both heal your traumas at approximately the same time. How likely is that, really? You are the rule, not the exception, for the most part. Are you willing to gamble the love you have with your primary partner on that 10% chance? Know that before you choose to go blindly into your twin flame connection or you'll likely regret your choice.