Close of Close Encounters put up for prize (6)
I believe the answer is:
esteem
'for prize' is the definition.
(synonyms)
'close of close encounters put up' is the wordplay.
'close of' suggests the final letters (the letter which ends or closes the word).
'encounters' becomes 'meets' ('meet' can be a synonym of 'encounter').
'put up' says the letters should be written in reverse.
The last letter of 'close' is 'e'.
'meets' in reverse letter order is 'steem'.
'e'+'steem'='ESTEEM'
(Other definitions for esteem that I've seen before include "Value highly" , "Favourable regard" , "credit" , "Hold in high regard and respect" , "High opinion, great respect" .)