Chap cross with country girl who's close to Douglas? (9)
I believe the answer is:
manxwoman
'girl who's close to douglas?' is the definition.
(woman from Isle of Man - Douglas is the capital)
'chap cross with country' is the wordplay.
'chap' becomes 'man' (chap can mean a man).
'cross' becomes 'x' (X is cross-shaped).
'with' becomes 'w' (abbreviation).
'country' becomes 'oman' (Oman is an example).
'man'+'x'+'w'+'oman'='MANXWOMAN'
(Other definitions for manxwoman that I've seen before include "lady from island" , "Wife of Douglas" .)