Bound to have left current US university (5)
I believe the answer is:
limit
'bound' is the definition.
(limit is a kind of bound)
'left current us university' is the wordplay.
'left' becomes 'l' (common abbreviation).
'current' becomes 'i' (symbol for electric current).
'us university' becomes 'mit' (I've seen this in other clues).
'l'+'i'+'mit'='LIMIT'
'to have' acts as a link.
(Other definitions for limit that I've seen before include "Confine to specific boundary" , "maximum number" , "Restrict - term" , "Extreme point" , "Utmost" .)