Good times for dodgy priest ending in ignominy (10)
I believe the answer is:
prosperity
'good times' is the definition.
(thesaurus)
'for dodgy priest ending in ignominy' is the wordplay.
'for' becomes 'pro' (as in being 'pro' or in favour of something).
'dodgy' indicates an anagram (a dodgy or wrong order of the letters).
'ending in' suggests the final letters.
The last letter of 'ignominy' is 'y'.
'priest' is an anagram of 'sperit'.
'pro'+'sperit'+'y'='PROSPERITY'
(Other definitions for prosperity that I've seen before include "wealth" , "Things going well" , "Financial success" .)