Peevishly irritable, but Clark not heartless (8)
I believe the answer is:
petulant
'peevishly irritable' is the definition.
(petulant can mean irritable or annoyed)
'clark not heartless' is the wordplay.
'clark' becomes 'petula' (singer Petula Clark).
'heartless' says to hollow out the word (remove centre letters).
'not' with its middle removed is 'nt'.
'petula'+'nt'='PETULANT'
'but' acts as a link.
(Other definitions for petulant that I've seen before include "Peevish, irritable" , "Sullen in a peevish way" , "Irritable, sullen" , "Peevish, inclined to complain" , "Pouting" .)