Chairman's supporter avoids area that's wet (5)
I believe the answer is:
moist
'that's wet' is the definition.
(similar in meaning)
'chairman's supporter avoids area' is the wordplay.
'chairman's supporter' becomes 'Maoist' (follower of Chairman Mao).
'avoids' is a deletion indicator.
'area' becomes 'a' (maths abbreviation).
'maoist' with 'a' taken away is 'MOIST'.
(Other definitions for moist that I've seen before include "Damp, humid" , "sloppy" , "lubricated" , "Slightly wet, damp" , "Affected by tears, perhaps" .)