Mature circle disowning Republican (6)
I believe the answer is:
evolve
'mature' is the definition.
(thesaurus)
'circle disowning republican' is the wordplay.
'circle' becomes 'revolve' (to revolve is to circle around).
'disowning' suggests deleting specific letters.
'republican' becomes 'r' (abbreviation).
'revolve' with 'r' removed is 'EVOLVE'.
(Other definitions for evolve that I've seen before include "Unfold" , "Undergo development or evolution" , "Change gradually to present condition" , "Slowly change" , "Grow slowly" .)