Nod back at professor (3)
I believe the answer is:
don
'professor' is the definition.
(term for a university professor)
'nod back at' is the wordplay.
'back' indicates one should take the final letters (the letter at the back).
'at' becomes 'on' (location).
The final letter of 'nod' is 'd'.
'd'+'on'='DON'
(Other definitions for don that I've seen before include "A mafia chief or Spanish lord" , "Spanish male title" , "put on > one of several rivers" , "Put on the learned man" , "Spanish gent or Mafia chief" .)