Formal:
* Yearn: To have a strong desire or longing for something.
* Ambit: To aim for something high or ambitious.
* Seek: To try to achieve or obtain something.
* Long: To desire something greatly.
* Aim: To direct one's efforts towards a specific goal.
Informal:
* Dream: To imagine or hope for something.
* Hope: To desire something with expectation of its fulfillment.
* Want: To have a strong desire for something.
* Wish: To express a desire for something.
The best synonym to use will depend on the context of your sentence and the level of formality you're aiming for.