Half-cut conservative tycoon oddly not prosperous (7)
I believe the answer is:
halcyon
'prosperous' is the definition.
(I know that prosperous can be written as halcyon)
'half-cut conservative tycoon oddly not' is the wordplay.
'cut' means to remove the last letter.
'conservative' becomes 'C' (UK political abbreviation).
'oddly not' indicates alternate letters (not the letters in odd-numbered positions).
The alternate letters of 'tycoon' are 'yon'.
'half' with its final letter taken off is 'hal'.
'hal'+'c'+'yon'='HALCYON'
(Other definitions for halcyon that I've seen before include "Prosperous" , "Happy and carefree" , "Tropical kingfisher" , "undisturbed" , "Happy, especially in the past" .)