Tenor's given award, mostly for opera (5)
I believe the answer is:
tosca
'opera' is the definition.
(Giacomo Puccini opera)
'tenor's given award mostly for' is the wordplay.
'tenor's' becomes 't's'.
'given' means one lot of letters goes inside another.
'award' becomes 'OM' (order of merit).
'mostly' means to remove the last letter.
'for' becomes 'ca' (I am not sure about this - if you are sure you should believe this answer much more).
'om' with its final letter removed is 'o'.
'ts' enclosing 'o' is 'tos'.
'tos'+'ca'='TOSCA'
(Other definitions for tosca that I've seen before include "opera singer" , "Puccini opera set in Rome" , "Coats off for Pucccni's opera" , "Puccini heroine" , "Puccini's Roman heroine" .)