Fool, silly chap in one type of headgear (5,3)
I believe the answer is:
cloth cap
'one type of headgear' is the definition.
'fool silly chap in' is the wordplay.
'fool' becomes 'clot' (I've seen this before**).
'silly' indicates anagramming the letters.
'in' indicates putting letters inside.
'chap' with letters rearranged gives 'hcap'.
'clot' placed into 'hcap' is 'CLOTH CAP'.
(Other definitions for cloth cap that I've seen before include "Stereotypical headgear for the working classes" , "Flat headgear" , "Flat hat" .)