Ponders about fellow student in secret movement (8)
I believe the answer is:
reflects
'ponders' is the definition.
(I know this)
'fellow student in secret movement' is the wordplay.
'fellow' becomes 'f' (abbreviation - of a society etc.).
'student' becomes 'l' (as in L-plates for learner drivers).
'in' is an insertion indicator.
'movement' indicates anagramming the letters (letters move around).
'f'+'l'='fl'
'secret' is an anagram of 'reects'.
'fl' inserted inside 'reects' is 'REFLECTS'.
'about' is the link.
(Other definitions for reflects that I've seen before include "shows in reverse" , "Mulls over" , "Mirrors or meditates" , "'Contemplates, considers (8)'" , "Thinks deeply like mirror?" .)