One who's lost faith in a petty officer, say (8)
I believe the answer is:
apostate
'one who's lost faith' is the definition.
'a petty officer say' is the wordplay.
'petty officer' becomes 'po' (naval abbreviation).
'say' becomes 'state' (synonyms).
'a'+'po'+'state'='APOSTATE'
'in' acts as a link.
(Other definitions for apostate that I've seen before include "Like rats" , "Dissenter" , "Julian was such" , "One deserting" , "Person who renounces former belief or loyalty" .)