It's from hilarity that this name is derived (6)
I believe the answer is:
hilary
'this name is derived' is the definition.
'Hilary' can be an answer for 'name'. I am not sure about the remainder of the definition.
'it's from hilarity' is the wordplay.
'from' is a deletion indicator.
'hilarity' with 'it' taken out is 'HILARY'.
'that' acts as a link.
Can you help me to learn more?
(Other definitions for hilary that I've seen before include "University term" , "The Spring legal term" , "Boy's or girl's name" , "Term < for a girl" , "girl or boy" .)