An ineffective person -- or Mayfair politician (4)
I believe the answer is:
wimp
'an ineffective person' is the definition.
(I've seen this before)
'mayfair politician' is the wordplay.
'mayfair' becomes 'wi'.
'politician' becomes 'mp'.
'wi'+'mp'='WIMP'
'or' acts as a link.
(Other definitions for wimp that I've seen before include "Informally, an ineffective man" , "Mummy's boy" , "Weak-willed person" , "Spineless type" , "doormat?" .)