to long, aim, or seek ambitiously; be eagerly desirous, esp. for something great or of high value (usually fol. by to, after, or an infinitive)

to aspire after literary immortality; to aspire to be a doctor.

Archaic . to rise up; soar; mount; tower.

adjective

ambitious , aspirant , eager , eager beaver * , endeavoring , enthusiastic , impassioned , longing , on the make , striving , wishful , would-be , zealous , emulous