Half of nine plus ten means nothing! (3)
I believe the answer is:
nix
'nothing' is the definition.
(nix can mean nothing)
'half of nine plus ten' is the wordplay.
'half of' indicates taking half.
'plus' is a charade indicator (letters next to each other).
'ten' becomes 'X' (Roman numeral).
'nine' with half the letters taken is 'ni'.
'ni'+'x'='NIX'
'means' acts as a link.
(Other definitions for nix that I've seen before include "Watch out for" , "Nothing (sl.)" , "Cancel" , "0" , "Spiteful water spirit" .)