Disrespectful cheek: loudly gasp about that (8)
I believe the answer is:
flippant
'disrespectful' is the definition.
(thesaurus)
'cheek loudly gasp about that' is the wordplay.
'cheek' becomes 'lip' (both can mean insolence or rudeness).
'loudly' becomes 'f' (short for forte - 'loud' in music).
'gasp' becomes 'pant' (synonyms).
'about that' indicates putting letters inside.
'f'+'pant'='fpant'
'lip' inserted within 'fpant' is 'FLIPPANT'.
(Other definitions for flippant that I've seen before include "showing disrespectful attitude" , "light" , "anything but serious" , "Impudent" , "Irreverent, saucy" .)