Egg on lecturer's visible (6)
I believe the answer is:
incite
'egg on' is the definition.
(synonyms)
'lecturer's visible' is the wordplay.
'lecturer's' indicates a 'sounds like' (homophone) clue (how it might sound in a lecture).
'visible' becomes 'insight' (something in sight is visible).
'insight' sounds like 'INCITE'.
(Other definitions for incite that I've seen before include "Provoke - stimulate" , "Move to action" , "'Stir up, provoke (6)'" , "Encourage, urge" , "Stir up (trouble)" .)