Problems exist over European student mobility system (7)
I believe the answer is:
erasmus
'european student mobility system' is the definition.
'problems exist over' is the wordplay.
'problems' becomes 'sums' (arithmetic problems).
'exist' becomes 'are' (I've seen this before).
'over' says the letters should be written in reverse.
'sums'+'are'='sumsare'
'sumsare' backwards is 'ERASMUS'.
(Other definitions for erasmus that I've seen before include "Learned person" , "Desiderius -, fifteenth and sixteenth century Dutch humanist" , "Fifteenth to sixteenth century Dutch humanist, use arms (anag.)" , "Renaissance scholar" , "Humanist critical of Church" .)