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