Pet of Roman priest removed from Beethoven opera (4)
I believe the answer is:
fido
'pet of roman' is the definition.
(common dog name from the Latin for faithful)
'priest removed from beethoven opera' is the wordplay.
'priest' becomes 'eli' (biblical figure).
'removed from' indicates named letters should be taken away.
'beethoven opera' becomes 'fidelio' (Fidelio is an opera by Ludwig van Beethoven).
'fidelio' with 'eli' taken away is 'FIDO'.
(Other definitions for fido that I've seen before include "it would disperse fog" , "Typical dog's name" , "Fog disperser" , "Dog perhaps" .)