He has a big head with a small hat to cover it (7)
I believe the answer is:
boaster
'he has a big head' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'with a small hat to cover it' is the wordplay.
'with' indicates putting letters inside.
'small' becomes 's' (abbreviation - e.g. clothes size).
'hat' becomes 'boer' (I am not sure about this - if you are sure you should believe this answer much more).
'to cover' means one lot of letters goes inside another.
'it' becomes ''t' (abbreviation. e.g. in 'tis).
'a'+'s'='as'
'as' going into 'boer' is 'boaser'.
'boaser' placed around 't' is 'BOASTER'.
Can you help me to learn more?
(Other definitions for boaster that I've seen before include "swanky one" , "One blows one's own trumpet" , "Braggart, blowhard" , "A sorbet for a braggart" , "Braggart, loud-mouth" .)