Old fine, overdue recently (2,4)
I believe the answer is:
of late
'recently' is the definition.
('of late' can be a synonym of 'recently')
'old fine overdue' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'fine' becomes 'f' (abbreviation).
'overdue' becomes 'late' ('late' can be similar in meaning to 'overdue').
'o'+'f'+'late'='OF LATE'
(Other definitions for of late that I've seen before include "In the recent past" , "Recently, not long agor" , "Alternative to 21 down" , "Not long ago, in recent times" , "recently, not long ago" .)