Thing not specified in legal term offering great amusement (8)
I believe the answer is:
hilarity
'great amusement' is the definition.
(I've seen this before)
'thing not specified in legal term' is the wordplay.
'thing not specified' becomes 'it' ('it' can refer to any object).
'in' means one lot of letters goes inside another.
'legal term' becomes 'hilary' (Hilary Term is a term or session in some courts).
'it' going inside 'hilary' is 'HILARITY'.
'offering' is the link.
(Other definitions for hilarity that I've seen before include "extreme amusement" , "Gaiety" , "Unrestrained mirth" , "Absence of gravity" , "fun" .)