Chronicle published about judge (7)
I believe the answer is:
narrate
'chronicle' is the definition.
(thesaurus)
'published about judge' is the wordplay.
'published' becomes 'ran' (running is a kind of publishing).
'about' says the letters should be written in reverse.
'judge' becomes 'rate' (rating is a kind of judging**).
'ran' in reverse letter order is 'nar'.
'nar'+'rate'='NARRATE'
(Other definitions for narrate that I've seen before include "Give a detailed account" , "'Recount, tell (7)'" , "Relay" , "recount events" , "Read" .)