Possibly sole apartment search (8)
I believe the answer is:
flatfish
'possibly sole' is the definition.
(I know that sole is a type of flatfish)
'apartment search' is the wordplay.
'apartment' becomes 'flat' (synonyms).
'search' becomes 'fish' (fishing is a kind of searching).
'flat'+'fish'='FLATFISH'
(Other definitions for flatfish that I've seen before include "Flounder, perhaps" , "could be a fluke" , "Perhaps sole" , "Sole, plaice etc" , "Swimmer" .)