Inspector with cut rejected by Underground worker (8)
I believe the answer is:
examiner
'inspector' is the definition.
(I know that inspector can be written as examiner)
'cut rejected by underground worker' is the wordplay.
'cut' becomes 'axe' (both can mean to cancel or remove).
'rejected' is a reversal indicator.
'by' is a charade indicator (letters next to each other).
'underground worker' becomes 'miner' (someone working underground in a mine).
'axe' backwards is 'exa'.
'exa'+'miner'='EXAMINER'
'with' is the link.
(Other definitions for examiner that I've seen before include "Test setter" , "Tester or inspector" , "Meaner XI (anag)" , "One looks for information" , "Person testing" .)