Leave out nothing in front of American Institute (4)
I believe the answer is:
omit
'leave out' is the definition.
('omit' can be a synonym of 'leave out')
'nothing in front of american institute' is the wordplay.
'nothing' becomes 'o' (looks like zero - 0).
'in front of' means one lot of letters go next to another.
'american institute' becomes 'mit' (I've seen this in other clues).
'o'+'mit'='OMIT'
(Other definitions for omit that I've seen before include "Leave out or undone" , "Exclude; veto" , "Leave out or exclude" , "Fail (to do something)" , "Leave out, do not include (4)" .)