Go up for prize (10)
I believe the answer is:
appreciate
I believe this clue is a double definition.
'go up' is the first definition.
(thesaurus)
'prize' is the second definition.
('appreciate' can be a synonym of 'prize')
'for' acts as a link.
(Other definitions for appreciate that I've seen before include "increase in price" , "(Of asset) rise in value" , "Take full account of" , "Be grateful for - rise in value" , "Enjoy" .)