Putin's puppets perhaps, being full of themselves (7,5)
I believe the answer is:
russian dolls
'full of themselves' is the definition.
I don't know anything about this answer so I can't judge whether it can be defined by this definition.
'putin's puppets perhaps being' is the wordplay.
I cannot really understand how this works, but
'puppets' could be 'dolls' (I've seen this in another clue) and 'dolls' is found within the answer.
'being' could be 'russian' (Russian is an example) and 'russian' is found in the answer.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Another definition for russian dolls that I've seen is " Hollow figurines, one inside another".)