Overdue, having time for coffee (5)
I believe the answer is:
latte
'coffee' is the definition.
(I've seen this before)
'overdue having time' is the wordplay.
'overdue' becomes 'late' ('late' can be similar in meaning to 'overdue').
'having' means one lot of letters goes inside another.
'time' becomes 't'.
'late' placed around '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" .)