You are never required to obtain additional destination tickets cards, even if you've completed the ones you have.
You have three options available to you:
- You could claim a route. Remember, routes are worth points, and nothing prevents someone from claiming routes once their destination tickets have been completed.
- You could pick new destination ticket cards. You might get lucky and get one or more that's already completed! If you don't think you're winning, this can be very effective.
- If you're unable or unwilling to take the above actions, you can effectively "pass" by drawing more transportation cards.