Let into Duke University after good grade (5)
I believe the answer is:
admit
'let' is the definition.
(I know that admit is a more specific form of the action let)
'duke university after good grade' is the wordplay.
'duke' becomes 'd' (abbreviation).
'university' becomes 'MIT' (Massachusetts Institute of Technology).
'after' is a charade indicator (letters next to each other).
'good grade' becomes 'a' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'd'+'mit'='dmit'
'dmit' put after 'a' is 'ADMIT'.
'into' is the link.
Can you help me to learn more?
(Other definitions for admit that I've seen before include "Confess - acknowledge" , "Grant entry to" , "Profess" , "Agree to the truth" , "Allow to enter; own up" .)