Live not disheartened by southern doctors? (9)
I believe the answer is:
residents
'doctors?' is the definition.
(I know this)
'live not disheartened by southern' is the wordplay.
'live' becomes 'reside' (synonyms).
'disheartened' suggests removing the centre.
'by' says to put letters next to each other.
'southern' becomes 's' (abbreviation).
'not' with its centre removed is 'nt'.
'reside'+'nt'+'s'='RESIDENTS'
(Other definitions for residents that I've seen before include "Lodgers" , "doctors" , "folk living down the road?" .)