Fellow outside acknowledges wife, an oppidan (10)

I believe the answer is:

townswoman

'an oppidan' is the definition.
(oppidan can mean an inhabitant of a town)

'fellow outside acknowledges wife' is the wordplay.
'fellow outside' becomes 't' (I am not sure about this - if you are sure you should believe this answer much more).
'acknowledges' becomes 'owns' (I've seen this in another clue).
'wife' becomes 'woman' (I've seen this in another clue).
't'+'owns'+'woman'='TOWNSWOMAN'

(Another definition for townswoman that I've seen is " Urban dweller".)

I've seen this clue in The Times.

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