Overweight cops left for dead (4)
I believe the answer is:
flat
'dead' is the definition.
(thesaurus)
'overweight cops left' is the wordplay.
'overweight' becomes 'fat' (similar in meaning).
'cops' means one lot of letters goes inside another (inserted letters are caught or copped).
'left' becomes 'l' (common abbreviation).
'fat' enclosing 'l' is 'FLAT'.
'for' is the link.
(Other definitions for flat that I've seen before include "No longer charged" , "Level - below the natural note" , "unexciting" , "Apartment - below the note" , "Dull; set of rooms" .)