Conservative grey hairdo finally shaven flat, this heralds cooler times (4,5)
I believe the answer is:
cold front
'finally shaven flat this heralds cooler times' is the definition.
The definition suggests a singular noun which matches the answer.
'conservative grey hairdo' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'grey' becomes 'old' (similar in meaning).
'hairdo' becomes 'front' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'c'+'old'+'front'='COLD FRONT'
Can you help me to learn more?
(Other definitions for cold front that I've seen before include "that might bring on a chill" , "sometimes a feature of weather forecast" , "which might change the weather" , "Meteorological boundary" , "freeze?" .)