Enjoy a party piece, not unknown, that's performed (10)
I believe the answer is:
appreciate
'enjoy' is the definition.
(I've seen this before)
'a party piece not unknown that's performed' is the wordplay.
'not' is a deletion indicator.
'unknown' becomes 'y' (algebra).
'that's performed' indicates an anagram.
'party'+'piece'='partypiece'
'partypiece' with 'y' removed is 'partpiece'.
'partpiece' anagrammed gives 'ppreciate'.
'a'+'ppreciate'='APPRECIATE'
(Other definitions for appreciate that I've seen before include "Treasure" , "gain in value" , "Take full account of" , "Increase in value" , "Be fully aware of" .)