Value more highly (6)
I believe the answer is:
prefer
'value more highly' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for prefer that I've seen before include "support" , "Like (something) better than another" , "Favour, like better" , "Tend to choose (one thing over another)" , "Like one better than another" .)