Some offenders in Fulham characterised by wrongdoing (6)
I believe the answer is:
sinful
'wrongdoing' is the definition.
(thesaurus)
'some offenders in fulham characterised' is the wordplay.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'SINFUL' is hidden in the letters of 'offenders in fulham characterised'.
'by' acts as a link.
(Other definitions for sinful that I've seen before include "Wicked, unholy" , "very unpleasant" , "Habitually wicked" , "Offensive to God" , "Fragrant climber" .)