Investigate cut-back at the colliery (7)
I believe the answer is:
examine
'investigate' is the definition.
(examining is a kind of investigating)
'cut-back at the colliery' is the wordplay.
'cut' becomes 'axe' (I've seen this before).
'back' says the letters should be written backwards.
'at' is a charade indicator (letters next to each other).
'the colliery' becomes 'mine' (I've seen this before).
'axe' back-to-front is 'exa'.
'exa'+'mine'='EXAMINE'
(Other definitions for examine that I've seen before include "vet" , "Question closely" , "Scrutinise, subject to test" , "Thoroughly inspect" , "Inspect, study" .)