Arguing and in debt by the end of December (6)
I believe the answer is:
rowing
'arguing' is the definition.
(I've seen this before)
'in debt by the end of december' is the wordplay.
'in debt' becomes 'owing' (I've seen this before).
'by' is a charade indicator (letters next to each other).
'the end of' says to take the final letters.
The last letter of 'december' is 'r'.
'owing' after 'r' is 'ROWING'.
'and' is the link.
(Other definitions for rowing that I've seen before include "Steven Redgrave's sport" , "Olympic sport; arguing" , "Sculling sport?" , "in dispute" , "Propelling boat with oars" .)