Slight quarrel about head of rare fish (5)
I believe the answer is:
sprat
'fish' is the definition.
(sprat is a kind of fish)
'slight quarrel about head of rare' is the wordplay.
'slight quarrel' becomes 'spat' (I've seen this before).
'about' means one lot of letters goes inside another.
'head of' suggests taking the first letters.
The initial letter of 'rare' is 'r'.
'spat' enclosing 'r' is 'SPRAT'.
(Other definitions for sprat that I've seen before include "Small fish (used to catch mackerel?)" , "Small fish, sardine, say" , "chap giving richer course material to the Dutch" , "Couple sharing meat" , "Jack, perhaps" .)