Offset by cousin Peter surprisingly receiving nothing (12)
I believe the answer is:
counterpoise
'offset' is the definition.
(thesaurus)
'cousin peter surprisingly receiving nothing' is the wordplay.
'surprisingly' indicates anagramming the letters.
'receiving' means one lot of letters goes inside another.
'nothing' becomes 'o' (looks like zero - 0).
'cousin'+'peter'='cousinpeter'
'cousinpeter' is an anagram of 'counterpise'.
'counterpise' placed around 'o' is 'COUNTERPOISE'.
'by' is the link.
(Other definitions for counterpoise that I've seen before include "balance" , "Offset" , "Balancing factor" , "Weight balancing another" .)