The late morning paper (4)
I believe the answer is:
exam
'paper' is the definition.
(I've seen this before)
'the late morning' is the wordplay.
'the late' becomes 'ex'.
'morning' becomes 'am'.
'ex'+'am'='EXAM'
(Other definitions for exam that I've seen before include "Written test" , "(Academic) test" , "Oral maybe" , "Something to sit" , "Set of questions evaluating skill or knowledge, in short" .)