Become drowsy, lecturer having turned up (3)
I believe the answer is:
nod
'become drowsy' is the definition.
(someone becoming drowsy might nod off)
'lecturer having turned up' is the wordplay.
'lecturer' becomes 'don' (I've seen this before).
'having turned up' says the letters should be written in reverse.
'don' back-to-front is 'NOD'.
(Other definitions for nod that I've seen before include "Silent assent" , "Tacit agreement" , "Gesture of agreement" , "Indicate agreement (or sleepiness!)" , "Show assent" .)