Primate's indolence, dismissing nothing (6)
I believe the answer is:
langur
'primate's' is the definition.
(I've seen this before)
'indolence dismissing nothing' is the wordplay.
'indolence' becomes 'languor' (I've seen this before).
'dismissing' is a deletion indicator.
'nothing' becomes 'o' (looks like zero - 0).
'languor' with 'o' taken away is 'LANGUR'.
(Other definitions for langur that I've seen before include "Long-tailed monkey" , "Long-tailed Asian primate; run gal (anagram)" .)