Operated in group with lots of intelligence — they're full of brains (6)
I believe the answer is:
crania
'intelligence they're full of brains' is the definition.
The definition suggests an adverb but the answer is not.
'operated in group with lots' is the wordplay.
'operated' becomes 'ran' ('run' can be a synonym of 'operate').
'in group' becomes 'ia' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'with' is a charade indicator (letters next to each other).
'lots' becomes 'c'.
'ran'+'ia'='rania'
'rania' put after 'c' is 'CRANIA'.
'of' acts as a link.
Can you help me to learn more?
(Another definition for crania that I've seen is " Skulls".)