Cut one in tough job-centre (6)
I believe the answer is:
hairdo
'cut' is the definition.
(I've seen this before)
'one in tough job-centre' is the wordplay.
'one' becomes 'i' (Roman numeral).
'in' is an insertion indicator.
'tough' becomes 'hard' (associated in meaning).
'centre' indicates the central letters.
The central letter of 'job' is 'o'.
'i' inserted within 'hard' is 'haird'.
'haird'+'o'='HAIRDO'
(Other definitions for hairdo that I've seen before include "Style for one's crowning glory" , "capital arrangement" , "Barnet" , "Bob, for one" , "Say, crew cut" .)