Central parts of Slough utterly peripheral (5)
I believe the answer is:
outer
'peripheral' is the definition.
(I've seen this before)
'central parts of slough utterly' is the wordplay.
'central parts of' says to take the centre.
'utterly' becomes 'ter' (I am not sure about this - if you are sure you should believe this answer much more).
The centre of 'slough' is 'ou'.
'ou'+'ter'='OUTER'
(Other definitions for outer that I've seen before include "Ring furthest from the bullseye" , "External kind of route" , "Away from the centre" , "Objective" , "External; peripheral" .)