Islander with French mother outside New Cross (7)
I believe the answer is:
manxman
'islander' is the definition.
(someone from the Isle of Man)
'french mother outside new cross' is the wordplay.
'french mother' becomes 'maman' ('mum' in French).
'outside' means one lot of letters goes inside another.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'cross' becomes 'x' (X is cross-shaped).
'n'+'x'='nx'
'maman' placed around 'nx' is 'MANXMAN'.
'with' acts as a link.
(Other definitions for manxman that I've seen before include "Islander" , "Chap from Douglas" , "Native of Douglas" .)