Overdue, having time for hot beverage (5)
I believe the answer is:
latte
'hot beverage' is the definition.
'overdue having time' is the wordplay.
'overdue' becomes 'late' (similar in meaning).
'having' is an insertion indicator.
'time' becomes 't' (abbreviation).
'late' placed around 't' is 'LATTE'.
'for' acts as a link.
(Other definitions for latte that I've seen before include "Espresso coffee and milk" , "Coffee served with hot milk" , "Type of coffee" , "Style of coffee" , "White coffee" .)