Chief relative going after first degree (3,6)
I believe the answer is:
top banana
'first degree' is the definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.
'chief relative going after' is the wordplay.
'chief' becomes 'top' ('top' can be a synonym of 'chief').
'relative going' becomes 'banana' (I can't explain this - if you can you should give a lot more credence to this answer).
'after' says to put letters next to each other.
'top'+'banana'='TOP BANANA'
Can you help me to learn more?
(Other definitions for top banana that I've seen before include "pick of the bunch?" , "1" , "Big cheese" , "Star comedian" , "leader" .)