Time to study philosopher? It's routine drudgery (9)
I believe the answer is:
treadmill
'routine drudgery' is the definition.
(I've seen this before)
'time to study philosopher?' is the wordplay.
'time' becomes 't'.
'to study' becomes 'read' ('read' can be a synonym of 'study').
'philosopher?' becomes 'mill' (I've seen this in other clues).
't'+'read'+'mill'='TREADMILL'
'it's' is the link.
(Other definitions for treadmill that I've seen before include "hard labour" , "Dreary repetitive work" , "Daily grind" , "Sportspeople utilise this" , "Situation of routine drudgery" .)