Better covering for the head (3)
I believe the answer is:
cap
I believe this is a double definition.
'better' is the first definition.
(I've seen this before)
'covering for the head' is the second definition.
(Other definitions for cap that I've seen before include "Dental work" , "Set limit to price increase - of headgear?" , "International sportsman" , "Beat; upper limit" , "Seal off oil-well" .)