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' says the answer is hidden in the clue.
'NOR' is hidden in the letters of 'ignorance'.
'out' is the 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" .)