Argument about rook and fish (5)
I believe the answer is:
sprat
'fish' is the definition.
(I know that sprat is a type of herring)
'argument about rook' is the wordplay.
'argument' becomes 'spat' (a spat is a disagreement or argument).
'about' indicates putting letters inside.
'rook' becomes 'R' (chess abbreviation).
'spat' enclosing 'r' is 'SPRAT'.
'and' is the link.
(Other definitions for sprat that I've seen before include "Strap up the small fish" , "Small marine fish" , "Small sea fish" , "'Set a . . . . . to catch a herring'" , "chap giving richer course material to the Dutch" .)