What postgraduates work for to a greater extent? (6,6)

I believe the answer is:

higher degree

I'm a little stuck... Click here to teach me more about this clue!

'what postgraduates work for' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'greater extent?' is the wordplay.
'greater' becomes 'higher' ('high' can be similar in meaning to 'great').
'extent?' becomes 'degree' (extent is a kind of degree).
'higher'+'degree'='HIGHER DEGREE'

'to a' acts as a link.

Can you help me to learn more?

I've seen this clue in The Globe and Mail.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.