Oarsman, perhaps, in argument with that woman, losing face (5)
I believe the answer is:
rower
'oarsman perhaps' is the definition.
(I know that rower is a type of rower)
'argument with that woman losing face' is the wordplay.
'argument' becomes 'row' (to row is to argue).
'with' means one lot of letters go next to another.
'that woman' becomes 'her' (her refers to a woman).
'losing face' means to remove the first letter.
'her' with its first letter taken off is 'er'.
'row'+'er'='ROWER'
'in' is the link.
(Other definitions for rower that I've seen before include "Oarswoman or oarsman" , "Perhaps stroke" , "Maybe one in eight" , "One who argues" , "He handles oars" .)