Tardy getting the first coffee (5)
I believe the answer is:
latte
'coffee' is the definition.
(type of coffee drink)
'tardy getting the first' is the wordplay.
'tardy' becomes 'late' (synonyms).
'getting' is an insertion indicator.
'the first' becomes 't' (1st letter of 'the').
'late' enclosing 't' is 'LATTE'.
(Other definitions for latte that I've seen before include "Espresso with frothy milk" , "Coffee beverage" , "Milky coffee drink" , "frothy cup" , "Frothy milky coffee" .)