Chap nursing old grievance (4)
I believe the answer is:
moan
'grievance' is the definition.
(thesaurus)
'chap nursing old' is the wordplay.
'chap' becomes 'Man' (chap can mean a man).
'nursing' indicates putting letters inside.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'man' going around 'o' is 'MOAN'.
(Other definitions for moan that I've seen before include "Keen" , "Express pain" , "Expression of suffering" , "Indicate pain" , "bellyache" .)