Hat given to old character (4)
I believe the answer is:
topi
'hat' is the definition.
(topi is a kind of hat)
'given to old character' is the wordplay.
'given' is a charade indicator (letters next to each other).
'old character' becomes 'pi' (pi is a kind of letter of the alphabet. I am not sure about the 'old' bit.).
'to'+'pi' is 'TOPI'.
Can you help me to learn more?
(Other definitions for topi that I've seen before include "Pith helmet" , "African antelope" , "cover in the heat" , "that goes ahead" , "Large antelope; pith hat" .)