Have lofty goals (6)
I believe the answer is:
aspire
'have lofty goals' 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 "Aim at high things" , "Have ambition or desire for praise" , "Hope (to do something)" , "Have a strong desire to reach an objective" , "Hanker" .)