Graduates have one large key to some letters (7)
I believe the answer is:
mailbag
'graduates have' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.
'one large key to some letters' is the wordplay.
'one large key' becomes 'bag' (I can't justify this - if you can you should give a lot more credence to this answer).
'to' means one lot of letters go next to another (I've seen this in other clues).
'some letters' becomes 'mail' (I've seen this in another clue).
'bag' put after 'mail' is 'MAILBAG'.
Can you help me to learn more?
(Other definitions for mailbag that I've seen before include "Sack for post" , "Postal sack" , "Post pouch" , "One sewn by convicts" , "Sack for carrying (American) letters" .)