Graduate uses a ruler for the cooking (6)
I believe the answer is:
baking
'the cooking' is the definition.
(baking is a kind of cooking)
'graduate uses a ruler' is the wordplay.
I cannot really see how this works, but
'graduate' could be 'ba' (someone with a Bachelor of Arts degree) and 'ba' is found within the answer.
'ruler' could be 'king' (king is a kind of ruler) and 'king' is located in the answer.
No letters remain.
This may be the basis of clue (or it may be nonsense).
'for' is the link.
Can you help me to learn more?
(Other definitions for baking that I've seen before include "Making bread, cake or pastry" , "For putting bun in the oven" , "Making bread, cake, etc." , "theme in Hollywood TV shows" , "Very hot; making bread" .)