'Pome' written on Cockney's locality (part of Bow) (5)
I believe the answer is:
hawse
'part of bow' is the definition.
(part of a ship's bow)
'pome written on cockney's locality' is the wordplay.
'pome' becomes 'haw' (a haw is a type of pome fruit).
'written on' means one lot of letters go next to another.
'cockney's locality' becomes 'se' (South East of England).
'haw'+'se'='HAWSE'
(Other definitions for hawse that I've seen before include "Part of vessel's bow" , "part of ship" .)