Carry on suits an eccentric (7)
I believe the answer is:
sustain
'carry on' is the definition.
(sustaining is a kind of carrying on)
'suits an eccentric' is the wordplay.
'eccentric' indicates an anagram.
'suits'+'an'='suitsan'
'suitsan' is an anagram of 'SUSTAIN'.
(Other definitions for sustain that I've seen before include "Support, keep going" , "Carry" , "Feed, nourish" , "Maintain" , "Bear (something's weight)" .)