Local loses name when backing musical (5)
I believe the answer is:
evita
'musical' is the definition.
(Andrew Lloyd Webber musical)
'local loses name when backing' is the wordplay.
'local' becomes 'native' (relating to a particular area).
'loses' suggests deleting specific letters.
'name' becomes 'n' (common abbreviation e.g. on forms).
'when backing' says the letters should be written backwards.
'native' with 'n' taken out is 'ative'.
'ative' in reverse letter order is 'EVITA'.
(Other definitions for evita that I've seen before include "Peron musical" , "1996 musical film, starring Madonna" , "Eva Peron" , "Nineteen Dn musical" , "Well-known musical" .)