Not in party that's best (5)
I believe the answer is:
outdo
'that's best' is the definition.
(synonyms)
'not in party' is the wordplay.
'not in' becomes 'out' ('out' is the opposite to 'in').
'party' becomes 'do' (do is a kind of party).
'out'+'do'='OUTDO'
(Other definitions for outdo that I've seen before include "Get the better of" , "Perform better than another" , "Surpass someone at something" , "Eclipse" , "Surpass - overshadow - excel" .)