Function Henry's supporting is hit (4)
I believe the answer is:
cosh
'hit' is the definition.
(coshing is a kind of hitting)
'function henry's supporting' is the wordplay.
'function' becomes 'cos' (mathematical function).
'henry' becomes 'H' (symbol for the unit of electrical inductance).
'supporting' means one lot of letters go next to another (in a down clue, some letters go below others).
'cos'+'h'='COSH'
'is' is the link.
(Other definitions for cosh that I've seen before include "Sap" , "Blunt weapon, often of hard rubber" , "From this, blow" , "Personal weapon" , "(Hit on the head with) a blunt weapon" .)