Jazz played just a little around mid-afternoon (4)
I believe the answer is:
trad
'jazz' is the definition.
(trad jazz is a type of jazz)
'little around mid-afternoon' is the wordplay.
'little' becomes 'tad' (both can mean a small amount).
'around' means one lot of letters goes inside another.
'mid' means to look at the middle letters (mid- can mean the middle of something).
The central letter of 'afternoon' is 'r'.
'tad' enclosing 'r' is 'TRAD'.
'played just a' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for trad that I've seen before include "Type of jazz or folk" , "music" , "Conventional (jazz)" , "(Of jazz) traditional" , "Classical (abbr)" .)