Young girl accepting tax cut gets upset by the apathy (9)
I believe the answer is:
lassitude
'the apathy' is the definition.
(lassitude is a kind of apathy)
'young girl accepting tax cut gets upset' is the wordplay.
'young girl' becomes 'lassie' (synonyms).
'accepting' indicates putting letters inside.
'tax' becomes 'duty' (duty is a kind of tax).
'cut' means to remove the last letter.
'gets upset' shows that the letters should be reversed in order (I've seen 'getting upset' mean this).
'duty' with its last letter taken away is 'dut'.
'dut' reversed gives 'tud'.
'lassie' placed around 'tud' is 'LASSITUDE'.
'by' is the link.
(Other definitions for lassitude that I've seen before include "slackness" , "Listlessness, fatigue" , "Is saluted with tiredness" , "30 [LETHARGY]" , "Lack of energy and enthusiasm" .)