Degree received at educational institution alluded to during American primary? (5,6)
I believe the answer is:
grade school
'american primary?' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'degree received at educational institution alluded to during' is the wordplay.
I cannot really see how this works, but
'degree' could be 'grade' (synonyms) and 'grade' is found within the answer.
'institution' could be 'school' (school is a kind of institution) and 'school' is found in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Another definition for grade school that I've seen is " Where American children learn".)