Repetitious new rite, with musical backing (9)
I believe the answer is:
iterative
'repetitious' is the definition.
(synonyms)
'new rite with musical backing' is the wordplay.
'new' indicates an anagram.
'with' says to put letters next to each other.
'musical' becomes 'evita' (Andrew Lloyd Webber musical).
'backing' shows that the letters should be reversed in order.
'evita' reversed gives 'ative'.
'rite' with letters rearranged gives 'iter'.
'iter'+'ative'='ITERATIVE'
(Other definitions for iterative that I've seen before include "Involving repetition" , "bears repeating" , "Relating to repetition" , "repeated" .)