Many tiny flies around Oscar providing invisibility (9)
I believe the answer is:
anonymity
'invisibility' is the definition.
'many tiny flies around oscar' is the wordplay.
'flies' indicates anagramming the letters.
'around' indicates putting letters inside.
'oscar' becomes 'o' (phonetic alphabet: alpha, bravo, charlie etc.).
'many'+'tiny'='manytiny'
'manytiny' with letters rearranged gives 'annymity'.
'annymity' enclosing 'o' is 'ANONYMITY'.
'providing' is the link.
(Other definitions for anonymity that I've seen before include "State of being unknown or nameless" , "State of not being known" .)