Old morning's tests! (5)
I believe the answer is:
exams
'tests' is the definition.
('exam' can be a synonym of 'test')
'old morning's' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'morning's' becomes 'am's' (as in 12:00 AM).
'ex'+'ams'='EXAMS'
(Other definitions for exams that I've seen before include "Cut up writing" , "More than one test" , "School tests" , "Set of exercises evaluating knowledge (abbr)" , "Important tests" .)