Tries desperately to take exam again (5)
I believe the answer is:
resit
'take exam again' is the definition.
(I've seen this before)
'tries desperately' is the wordplay.
'desperately' is an anagram indicator.
'tries' with letters rearranged gives 'RESIT'.
'to' is the link.
(Other definitions for resit that I've seen before include "repeated test" , "Take examination again" , "second try at test" , "later exam" , "tested again" .)