Sound demeanour for one who'll succeed (4)
I believe the answer is:
heir
'one who'll succeed' is the definition.
(an heir is someone's successor)
'sound demeanour' is the wordplay.
'sound' shows a homophone (sound like).
'demeanour' becomes 'air' (air is a kind of demeanour).
'air' is a homophone of 'HEIR'.
'for' is the link.
(Other definitions for heir that I've seen before include "Acknowledged beneficiary" , "Expected successor" , "One expected to succeed?" , "Beneficiary, inheritor" , "Someone expected to inherit" .)