One holding lecture in public (12)
I believe the answer is:
unclassified
'public' is the definition.
(as opposed to classified, top secret)
'one holding lecture' is the wordplay.
'one' becomes 'unified' (I've seen this in another clue).
'holding' is an insertion indicator.
'lecture' becomes 'class' (academic class).
'unified' enclosing 'class' is 'UNCLASSIFIED'.
'in' acts as a link.
(Other definitions for unclassified that I've seen before include "Not given category" , "in no particular order" .)