Fresher in Cambridge saw science tutor last of all (5)
I believe the answer is:
newer
'fresher' is the definition.
('new' is associated in meaning with 'fresh')
'in cambridge saw science tutor last of all' is the wordplay.
'last of all' indicates one should take the final letters.
The final letters of 'in cambridge saw science tutor' are 'NEWER'.
(Other definitions for newer that I've seen before include "More current" , "More up-to-date" , "More modern" , "More recent" , "More pristine or recently invented" .)