Cleaner in university getting in before rector (5)
I believe the answer is:
purer
'cleaner' is the definition.
('pure' can be similar in meaning to 'clean')
'university getting in before rector' is the wordplay.
'university' becomes 'U' (abbreviation for university).
'getting in' indicates putting letters inside.
'before' becomes 'pre' (prefix meaning 'before').
'rector' becomes 'r'.
'u' placed within 'pre' is 'pure'.
'pure'+'r'='PURER'
'in' acts as a link.
(Other definitions for purer that I've seen before include "Less adulterated" , "cleaner" , "More chaste" , "more clean" , "Less immoral" .)