Possible Clues:

• Yale, for five U.S. presidents
• Grad's school
• 22 stream, a term employed at university
• Commencement hymn
• Old university has to adapt, providing accommodation for people with higher degrees
• As a learner, am sent down, having wasted a term — here?
• One's school, college or university
• 63-Across?
• Old university needs to adapt, graduate repeatedly admitted
• UCLA's "Hail to the Hills of Westwood," e.g.