Analgesic for month spent with English student (7)
I believe the answer is:
menthol
'analgesic' is the definition.
(I've seen this before)
'month spent with english student' is the wordplay.
'spent with' indicates an anagram.
'english' becomes 'e' (abbreviation).
'student' becomes 'l' (as in L-plates for learner drivers).
'month' anagrammed with 'e' can make 'mentho'.
'mentho'+'l'='MENTHOL'
'for' is the link.
(Other definitions for menthol that I've seen before include "Peppermint camphor" , "mild analgesic" , "Substance from peppermint oil used as flavouring." , "medicinal compound" , "Peppermint oil derivative" .)