Synonyms for Aspire:

n.

look for, long, lust after, have your heart set on (doing) something, crave. dream. start. aspire (noun)
shoot for, aim.
yearn (noun)
try.

v.

aim, hope (verb)
dream, pursue, want, wish, long, seek, desire, yearn, strive, try, crave.
cognition (verb)
shoot for, aim.
hope (verb)
presume, yearn, believe, anticipate, contemplate, rely, await, desire, want, trust, assume, hope, wish, expect, dream of.
petition (verb)
claim, bid, compete, petition, apply.
pursue (verb)
seek, pursue, harry, chase, search, stalk, tail, dog, sleuth, aim, quest, follow, track, intend, hunt, undertake, endeavor, strive, trail.

Other synonyms:

look for, try, crave. long. desire
want.
long
dream of, yearn.
Other relevant words:
try, long, crave, shoot for, dream, lust after.

Usage examples for aspire

  1. We must not even aspire to glory, for a civil war affords none. – A Book of Golden Deeds by Charlotte M. Yonge
  2. He had no other interests, he had no wife, he did not any longer even aspire to office. – The Turnstile by A. E. W. (Alfred Edward Woodley) Mason