Delighted overdue book's lost (6)
I believe the answer is:
elated
'delighted' is the definition.
(I've seen this before)
'overdue book's lost' is the wordplay.
'overdue' becomes 'belated' (I've seen this before).
'book' becomes 'b' (abbreviation for book).
'lost' suggests deleting specific letters.
'belated' with 'b' taken away is 'ELATED'.
(Other definitions for elated that I've seen before include "Overjoyed, in high spirits" , "Overjoyed, happy and excited" , "Jubilant, happy and excited" , "Puffed with success" , "Delighted, ecstatic" .)