Have high ambitions (6)
I believe the answer is:
aspire
'have high ambitions' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for aspire that I've seen before include "Hope (to do something)" , "Persia (anag.)" , "Hope, dream" , "Aim at, work towards" , "Aim, shoot for" .)