A girl not without heart, but peevishly impatient (8)

I believe the answer is:

petulant

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'peevishly impatient' is the definition.
'petulant' can be an answer for 'impatient' (thesaurus). I am not certain of the 'peevishly' bit.

'a girl not without heart' is the wordplay.
'a girl' becomes 'petula' (I can't justify this - if you can you should believe this answer much more).
'without heart' says to hollow out the word (remove centre letters).
'not' with its middle removed is 'nt'.
'petula'+'nt'='PETULANT'

'but' is the link.

Can you help me to learn more?

(Other definitions for petulant that I've seen before include "Irritable, sullen" , "Querulous and demanding" , "Easily provoked" , "Fractious, peevish" , "Fractious, pouty" .)

I've seen this clue in The Irish News.

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