Starts to drizzle awfully, new kit wet (4)
I believe the answer is:
dank
'wet' is the definition.
('dank' can be similar in meaning to 'wet')
'starts to drizzle awfully new kit' is the wordplay.
'starts to' indicates taking the first letters.
The first letters of 'drizzle awfully new kit' is 'DANK'.
(Other definitions for dank that I've seen before include "Cold and moist" , "Chilly and clammy" , "Clammy, damp" , "Unpleasantly cool and humid" , "Unpleasantly cold and humid" .)