Senior lecturer back having received low grades (6)
I believe the answer is:
reader
'senior lecturer' is the definition.
(I've seen this before)
'back having received low grades' is the wordplay.
'back' becomes 'rear' ('rear' can be a synonym of 'back').
'having received' means one lot of letters goes inside another.
'low grades' becomes 'de' (I've seen this in other clues).
'rear' placed around 'de' is 'READER'.
(Other definitions for reader that I've seen before include "University academic" , "University lecturer; book of educational extracts" , "Learning book" , "Senior lecturer" , "(User of) standard textbook" .)