Some fat surrounding cord (7)
I believe the answer is:
lanyard
'cord' is the definition.
(lanyard is a kind of cord)
'some fat surrounding' is the wordplay.
'some' becomes 'any' ('any' can be similar in meaning to 'some').
'fat' becomes 'lard' (I've seen this before).
'surrounding' is an insertion indicator.
'any' placed into 'lard' is 'LANYARD'.
(Other definitions for lanyard that I've seen before include "Dawdler" , "Cord worn round neck" , "Rope on ship's rigging" , "Neck cord holding whistle" , "Line for extending or fastening ship's rigging" .)