One visiting woman's eldest son perhaps (4)
I believe the answer is:
heir
'eldest son perhaps' is the definition.
'one visiting woman's' is the wordplay.
'one' becomes 'i' (Roman numeral).
'visiting' means one lot of letters goes inside another.
'woman' becomes 'her' (**).
'i' going inside 'her' is 'HEIR'.
(Other definitions for heir that I've seen before include "One due to inherit" , "Person who succeeds" , "One hoping to succeed" , "one's to inherit throne!" , "Acknowledged beneficiary" .)