Make early sporting exit, but not be “distressed” (4,3,3)

I believe the answer is:

miss the cut

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

'early sporting exit but not be distressed' is the definition.
I don't know anything about this answer so I can't tell whether it can be defined by this definition.

'make' is the wordplay.
I cannot quite understand how this works, but
'make' could be 'cut' (cutting is a kind of making) and 'cut' is located in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in The Times.

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.