Putin's puppets perhaps, being full of themselves (7,5)
I believe the answer is:
russian dolls
'full of themselves' is the definition.
I know nothing about this answer so I can't judge whether this works.
'putin's puppets perhaps being' is the wordplay.
I cannot quite see how this works, but
'puppets' could be 'dolls' (I've seen this in another clue) and 'dolls' is found in the answer.
'being' could be 'russian' (Russian is an example) and 'russian' is found within the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Another definition for russian dolls that I've seen is " Hollow figurines, one inside another".)