Dance with student also involved in tempestuous affair (8,5)
I believe the answer is:
highland fling
'dance' is the definition.
(I know that highland fling is a type of Scottish reel)
'student also involved in tempestuous affair' is the wordplay.
'student' becomes 'l' (as in L-plates for learner drivers).
'also' becomes 'and' (I've seen this before).
'involved in' is an insertion indicator.
'tempestuous' becomes 'high'.
'affair' becomes 'fling' (a fling is a romantic affair).
'l'+'and'='land'
'high'+'fling'='highfling'
'land' going inside 'highfling' is 'HIGHLAND FLING'.
'with' acts as a link.
(Other definitions for highland fling that I've seen before include "Scottish dance (involving a caber?)" , "Energetic measure" , "Dance (a Scottish affair?)" , "Traditional Scottish dance" , "Scottish solo dance" .)