Student finally gets to study philosopher — a dreary routine! (9)
I believe the answer is:
treadmill
'a dreary routine' is the definition.
(I've seen this before)
'student finally gets to study philosopher' is the wordplay.
'student finally' becomes 't' (I can't explain this - if you can you should give a lot more credence to this answer).
'gets' means one lot of letters go next to another.
'to study' becomes 'read' (synonyms).
'philosopher' becomes 'mill' (John Stuart Mill).
't'+'read'+'mill'='TREADMILL'
Can you help me to learn more?
(Other definitions for treadmill that I've seen before include "Walking or running exercise device" , "Endlessly tedious job" , "tedious routine" , "day-to-day grind" , "Wearisome routine" .)