'Turbulent priest' due for infamy (9)
I believe the answer is:
disrepute
'infamy' is the definition.
(thesaurus)
'turbulent priest due' is the wordplay.
'turbulent' is an anagram indicator.
'priest'+'due'='priestdue'
'priestdue' with letters rearranged gives 'DISREPUTE'.
'for' is the link.
(Other definitions for disrepute that I've seen before include "get a bad name" , "Ignominy" , "Ill fame" , "State of being held in low public esteem" .)