Stood up cold topless Dutch egotist (9)
I believe the answer is:
narcissus
'egotist' is the definition.
(I have seen 'Mythical egotist' mean 'narcissus' so perhaps 'egotist' could also mean 'narcissus')
'stood up cold topless dutch' is the wordplay.
'stood' becomes 'ran' (both can mean ran for office**).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'cold' becomes 'c' (eg on taps).
'topless' means to remove the first letter.
'dutch' becomes 'missus' (I've seen this before).
'ran' in reverse letter order is 'nar'.
'missus' with its first letter taken off is 'issus'.
'nar'+'c'+'issus'='NARCISSUS'
(Other definitions for narcissus that I've seen before include "Daffodil-like bulb" , "Greek youth who fell in love with his own reflection" , "Self-regarding youth" , "Mythical egotist" , "Small daffodil" .)