American: that woman's escort (5)
I believe the answer is:
usher
'escort' is the definition.
(I know that usher is a type of escort)
'american that woman's' is the wordplay.
'american' becomes 'us' (abbreviation for United States).
'that woman' becomes 'her' (her refers to a woman).
'us'+'her'='USHER'
(Other definitions for usher that I've seen before include "Escort (to a seat)" , "'The Fall of the House of -----', Edgar Allan Poe" , "Doorman or seat guide" , "Show in - escort" , "Person who shows one to a seat" .)