Poet's finished penning page, a lyrical piece (5)
I believe the answer is:
opera
'lyrical piece' is the definition.
(piece of music with lyrics)
'poet's finished penning page a' is the wordplay.
'poet's finished' becomes 'o'er' (poetic spelling of 'over').
'penning' indicates putting letters inside.
'page' becomes 'p'.
'oer' enclosing 'p' is 'oper'.
'oper'+'a'='OPERA'
(Other definitions for opera that I've seen before include "Eg, Don Giovanni" , "Drama or comedy set to music" , "Norma, say" , "Fidelio for instance" , "Die Meistersinger is one" .)