Well known to have done wrong, being out to start trouble (5)
I believe the answer is:
noted
'well known' is the definition.
(I've seen this in another clue)
'done wrong being out to start trouble' is the wordplay.
'wrong' indicates an anagram.
'being out' indicates putting letters inside.
'to start' suggests taking the first letters.
The initial letter of 'trouble' is 't'.
'done' is an anagram of 'noed'.
'noed' going around 't' is 'NOTED'.
'to have' is the link.
(Other definitions for noted that I've seen before include "Scores like this" , "Scored" , "Gaiter; oyster spawn" , "Indicated" , "Famed" .)