American with his woman, perhaps overseas (6)
I believe the answer is:
abroad
'overseas' is the definition.
(synonyms)
'american with his woman' is the wordplay.
I cannot quite understand how this works, but
'american' could be 'a' (common abbreviation - e.g. in organisation names) and 'a' is present in the answer.
'woman' could be 'broad' (broad is a kind of woman) and 'broad' is present in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
'perhaps' is the link.
Can you help me to learn more?
(Other definitions for abroad that I've seen before include "In another country, not at home" , "At large - overseas" , "in France, say" , "Europe, for example" , "At large; widely current" .)