Cockney’s religious, embracing writer publicly (6)
I believe the answer is:
openly
'publicly' is the definition.
(thesaurus)
'cockney's religious embracing writer' is the wordplay.
'cockney's religious' becomes ''oly' ('holy' - I've seen this in other clues - said with a cockney accent, dropping the 'H').
'embracing' is an insertion indicator.
'writer' becomes 'pen' (something which writes).
'oly' enclosing 'pen' is 'OPENLY'.
(Other definitions for openly that I've seen before include "Candidly, without concealment." , "Above board" , "In public" , "Overtly" , "Frankly, honestly" .)