In back with Carson a former Soviet leader (6)
I believe the answer is:
nikita
'former soviet leader' is the definition.
The definition suggests a singular noun which matches the answer.
'in back with carson a' is the wordplay.
'back' is a reversal indicator.
'with' is a charade indicator (letters next to each other).
'carson' becomes 'kit' (I've seen this in another clue).
'in' written backwards gives 'ni'.
'ni'+'kit'+'a'='NIKITA'
Can you help me to learn more?
(Another definition for nikita that I've seen is " ... Khrushchev".)