Soon get a French veto (4)
I believe the answer is:
Here is my best explanation:
'soon' is the definition.
('anon' can be a synonym of 'soon')
'get a french veto' is the subsidiary indication.
'get' means one lot of letters go next to another.
'french veto' becomes 'non' (French for 'no', a word which might veto something).
'a' put next to 'non' is 'anon'.
(Other definitions for anon that I've seen before include "Of unknown name (abbr)", "Soon - nobody knows me", "Shortly; unknown", "Of unknown authorship", "Mystery writer", "Soon or presently", "Well-published writer", "Incognito (abbrev)", "Nameless (abbr.); soon" and "Unknown (abbr)".)