Cold rush taking one's discipline (8)
I believe the answer is:
chastise
'discipline' is the definition.
(thesaurus)
'cold rush taking one's' is the wordplay.
'cold' becomes 'c' (eg on taps).
'rush' becomes 'haste' ('haste' can be a synonym of 'rush'**).
'taking' indicates putting letters inside.
'one's' becomes 'is' (roman numeral).
'haste' enclosing 'is' is 'hastise'.
'c'+'hastise'='CHASTISE'
(Other definitions for chastise that I've seen before include "Inflict physical corrective treatment" , "Whip perhaps" , "Teach Sis to scold" , "Punished severely" , "Berate" .)