Written test is old in the morning (4)
I believe the answer is:
exam
'written test' is the definition.
(I've seen this before)
'old in the morning' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'in the morning' becomes 'am' (AM on a clock).
'ex'+'am'='EXAM'
'is' is the link.
(Other definitions for exam that I've seen before include "School test (colloq.)" , "One might be taken for English" , "Scholastic test" , "Important test" , "Test (abbr)" .)