Verbal demand to cover student’s reading light (7)
I believe the answer is:
glimmer
'light' is the definition.
(I have seen 'Faint light ' mean 'glimmer' so perhaps 'light' could also mean 'glimmer')
'verbal demand to cover student's reading' is the wordplay.
'verbal demand' becomes 'gimme' (I can't explain this - if you can you should believe this answer much more).
'to cover' means one lot of letters goes inside another.
'student' becomes 'l' (as in L-plates for learner drivers).
'reading' becomes 'r' (one of the traditional three R's of education).
'gimme' placed around 'l' is 'glimme'.
'glimme'+'r'='GLIMMER'
Can you help me to learn more?
(Other definitions for glimmer that I've seen before include "Faint wavering light" , "Flicker" , "Shine faintly and waveringly" , "Intimation (of hope?)" , "Faint sign" .)