Snake oil primarily accepted by graduate (3)
I believe the answer is:
boa
'snake' is the definition.
(boa is a kind of snake)
'oil primarily accepted by graduate' is the wordplay.
'primarily' indicates taking the first letters.
'accepted by' means one lot of letters goes inside another.
'graduate' becomes 'ba' (**).
The initial letter of 'oil' is 'o'.
'o' going into 'ba' is 'BOA'.
(Other definitions for boa that I've seen before include "that's dangerous for South Americans" , "Large snake provides a neck decoration" , "Long, thin, feathery scarf" , "Wrap" , "feathers around the neck?" .)