To win, you must move your piece to the same location as the Time Breaker, declare that they are under arrest, and return with them to the TRA tile before any of your opponents.
If your piece moves to the TRA tile with the Time Breaker in tow first, you win! Congratulations!
If someone causes the Time Breaker to move to the TRA tile unaccompanied, it means they turned themselves in, so no one gets credit for making the arrest, and thus nobody wins. This is true even if the Time Breaker and a player’s piece both return to the TRA at the same time, but not together.
For example, if the Time Breaker is on a tile adjacent to the TRA, and someone plays Shut and Run, they could choose to move the Time Breaker to the TRA. Since all players on the crashed gate are bounced back to the TRA space, a player who had the Time Breaker in custody will be moved to the TRA tile just after the Time Breaker arrives. Such a player gets back to HQ just in time to watch as the Time Breaker surrenders.