Dressed up to hear a bit of Puccini? This may be part of it (5,3)
I believe the answer is:
opera hat
'it' is the definition.
The definition suggests a singular noun which matches the answer.
'dressed up to hear a bit of puccini? this may be part' is the wordplay.
'dressed up' indicates anagramming the letters.
'bit of' suggests taking the first letters.
'this may be' is an anagram indicator.
'part' indicates putting letters inside (the inserted letters split open or part the word).
The first letter of 'puccini' is 'p'.
'hear'+'a'+'p'='hearap'
'hearap' with letters rearranged gives 'peraha'.
'to' is an anagram of 'ot'.
'ot' enclosing 'peraha' is 'OPERA-HAT'.
'of' acts as a link.
(Other definitions for opera hat that I've seen before include "collapsible accessory - atop him surely?" , "garment in theatre?" , "that can be altered to flatter profile" , "Formal theatre wear" , "Lid that collapses" .)