Like that woman Jane who went out with Paul? (5)
I believe the answer is:
asher
'jane who went out with paul?' is the definition.
(Jane Asher, ex-girlfriend of Paul McCartney)
'like that woman' is the wordplay.
'like' becomes 'as'.
'that woman' becomes 'her' (I've seen this before**).
'as'+'her'='ASHER'
(Other definitions for asher that I've seen before include "Jane --, actress and novelist" , "tribe" , "Hebrew patriarch" , "Jacob's son" , "15 [JANE] the cake decorator" .)