Neither out of ignorance (3)
I believe the answer is:
nor
'neither' is the definition.
(eg in the phrase 'neither do I')
'of ignorance' is the wordplay.
'of' indicates a hidden word.
'NOR' can be found hidden inside 'ignorance'.
'out' acts as a link.
(Other definitions for nor that I've seen before include "And not; Norman (abbr.)" , "Common conjunction, goes with neither" , "Neither one ... the other" , "logic circuit" , "Negative word" .)