Some regularly fell back for tests (5)
I believe the answer is:
exams
'tests' is the definition.
('exam' can be a synonym of 'test')
'some regularly fell back' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'fell' becomes 'axe' (I've seen this before).
'back' says the letters should be written backwards.
The alternate letters of 'some' are 'sm'.
'sm'+'axe'='smaxe'
'smaxe' in reverse letter order is 'EXAMS'.
'for' is the link.
(Other definitions for exams that I've seen before include "Set of exercises evaluating knowledge (abbr)" , "School tests" , "Tests, in short" , "Cut up writing" , "papers" .)