Overdue, with time for a coffee (5)
I believe the answer is:
latte
'coffee' is the definition.
(type of coffee drink)
'overdue with time' is the wordplay.
'overdue' becomes 'late' (similar in meaning).
'with' is an insertion indicator.
'time' becomes 't' (abbreviation).
'late' enclosing 't' is 'LATTE'.
'for a' is the link.
(Other definitions for latte that I've seen before include "Kind of espresso coffee" , "White coffee" , "hot drink" , "Coffee served with hot milk" , "Coffee with a topping of frothed steamed milk" .)