Beloved party embraced by American lefty (6)
I believe the answer is:
adored
'beloved' is the definition.
(I've seen this in another clue)
'party embraced by american lefty' is the wordplay.
'party' becomes 'do' (do can informally mean a party).
'embraced by' is an insertion indicator.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'lefty' becomes 'red' (red can mean a left-wing person).
'a'+'red'='ared'
'do' inserted within 'ared' is 'ADORED'.
(Other definitions for adored that I've seen before include "Worshipped and venerated" , "Worshipped, loved" , "Loved deeply" , "Much loved" , "Cherished" .)