Jazz age was best, conclusively, for enthusiasm (4)
I believe the answer is:
zest
'for enthusiasm' is the definition.
(zest can mean enthusiasm or eagerness)
'jazz age was best conclusively' is the wordplay.
'conclusively' indicates one should take the final letters (the letter which concludes the word).
The final letters of 'jazz age was best' are 'ZEST'.
(Other definitions for zest that I've seen before include "Verve, gusto" , "Orange-peel" , "Relish, enthusiasm" , "Piquancy - fruit rind" , "Enthusiasm or outer skin of citrus fruit" .)