Aim at higher things (6)
I believe the answer is:
aspire
'aim at higher things' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for aspire that I've seen before include "Have ambition or desire for praise" , "Aim at, work towards" , "Have a strong desire to reach an objective" , "Have an ambitious plan or a lofty goal" , "Have lofty aims" .)