One offers prayers to monarchical bust (5,8)
I believe the answer is:
roman catholic
'one offers prayers to monarchical bust' is the definition.
I can't tell whether this definition defines the answer.
'to monarchical bust' is the wordplay.
'bust' indicates an anagram.
'to'+'monarchical'='tomonarchical'
'tomonarchical' anagrammed gives 'ROMAN CATHOLIC'.
Can you help me to learn more?
(Other definitions for roman catholic that I've seen before include "RC in full" , "Its head is the Pope" , "Church member" , "Religious believer" .)