A tiny bit dry wearing hat (6)
I believe the answer is:
tittle
'a tiny bit' is the definition.
(I've seen this before)
'dry wearing hat' is the wordplay.
'dry' becomes 'tt' (abbreviation for teetotal).
'wearing' means one lot of letters goes inside another.
'hat' becomes 'tile' (I've seen this before).
'tt' going into 'tile' is 'TITTLE'.
(Other definitions for tittle that I've seen before include "Tiny printed mark" , "A printed dot as in i" , "Companion to jot" , "Smallest part (after a jot?)" , "A tiny bit" .)