Tax - it's ignored in frivolity (4)
I believe the answer is:
levy
'tax' is the definition.
(I know that tax is a more specific form of levy)
'it's ignored in frivolity' is the wordplay.
'ignored in' suggests deleting specific letters.
'frivolity' becomes 'levity' (levity is a kind of frivolity).
'levity' with 'it' removed is 'LEVY'.
(Other definitions for levy that I've seen before include "Charge a fee or tax" , "Tax raised" , "enlisted troops" , "Raise (money, troops)" , "tax money" .)