Hot woman turning up with hair dye (5)
I believe the answer is:
henna
'hair dye' is the definition.
(henna is a kind of hair dye)
'hot woman turning up' is the wordplay.
'hot' becomes 'h' (abbreviation, eg on taps).
'woman' becomes 'anne' (woman's name).
'turning up' says the letters should be written in reverse.
'anne' back-to-front is 'enna'.
'h'+'enna'='HENNA'
'with' is the link.
(Other definitions for henna that I've seen before include "natural colour?" , "hair colour?" , "hair colouring" , "Local colour" , "A shrub, its red dye" .)