Cheap tat I chucked out, being indifferent (9)
I believe the answer is:
apathetic
'being indifferent' is the definition.
('apathetic' can be a synonym of 'indifferent')
'cheap tat i chucked' is the wordplay.
'chucked' indicates anagramming the letters (letters chucked around).
'cheap'+'tat'+'i'='cheaptati'
'cheaptati' with letters rearranged gives 'APATHETIC'.
'out' acts as a link.
(Other definitions for apathetic that I've seen before include "showing no enthusiasm" , "Listless, lacking in interest" , "cool?" , "Having little interest, indifferent" , "disinclined to act" .)