Carping is fitting following constant promises to pay (8)
I believe the answer is:
captious
'carping' is the definition.
(I've seen this before)
'fitting following constant promises to pay' is the wordplay.
'fitting' becomes 'apt' (I've seen this before).
'following' means one lot of letters go next to another.
'constant' becomes 'c' (mathematical abbreviation).
'promises to pay' becomes 'ious' (more than one iou).
'apt' after 'c' is 'capt'.
'capt'+'ious'='CAPTIOUS'
'is' is the link.
(Other definitions for captious that I've seen before include "Fault-finding" , "Tending to find fault" , "Carping" , "Raising petty objections" , "Inclined to find fault" .)