Dying to hear part of National Lear soliloquy (3,4)
I believe the answer is:
all ears
'dying to hear' is the definition.
(if you're 'all ears' you're desperate to hear)
'part of national lear soliloquy' is the wordplay.
'part of' indicates a hidden word.
'ALL EARS' can be found hidden inside 'national lear soliloquy'.
(Other definitions for all ears that I've seen before include ".Listening very intently" , "description of cornfield?" , "Very alert" , "Listening attentively" , "Being very attentive" .)