Cut up over end of term test (4)
I believe the answer is:
exam
'test' is the definition.
('exam' can be a synonym of 'test')
'cut up over end of term' is the wordplay.
'cut' becomes 'axe' (I've seen this before**).
'up' is a reversal indicator (in down clue: letters go upwards).
'over' is a charade indicator (letters next to each other).
'end of' indicates one should take the final letters.
The last letter of 'term' is 'm'.
'axe' in reverse letter order is 'exa'.
'exa'+'m'='EXAM'
(Other definitions for exam that I've seen before include "Written test" , "'Test, in short (4)'" , "School test (colloq.)" , "Student test" , "paper" .)