Tests after some oddly fell back (5)
I believe the answer is:
exams
'tests' is the definition.
('exam' can be a synonym of 'test')
'some oddly fell back' is the wordplay.
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
'fell' becomes 'axe' (I've seen this before).
'back' shows that the letters should be reversed in order.
The alternating letters of 'some' are 'sm'.
'sm'+'axe'='smaxe'
'smaxe' back-to-front is 'EXAMS'.
'after' acts as a link.
(Other definitions for exams that I've seen before include "Cut up writing" , "Tests, in short" , "Student assessments" , "papers" , "summer term commitment?" .)