Get up carrying new hair dye (5)
I believe the answer is:
rinse
'hair dye' is the definition.
(rinse is a kind of hair dye)
'get up carrying new' is the wordplay.
'get up' becomes 'rise' (synonyms).
'carrying' is an insertion indicator.
'new' becomes 'n' (abbreviation as in New Testament NT).
'rise' enclosing 'n' is 'RINSE'.
(Other definitions for rinse that I've seen before include "Hair colourant" , "blue one on top?" , "Wash without using soap" , "Wash off surface dirt" , "Cleanse in water" .)