Pump up, Jeez, boring grammar school weed (3,4)

I believe the answer is:

gym shoe

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

This clue might be a double definition.

'pump up' is the first definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Maybe there's a link between them I don't understand?

'jeez boring grammar school weed' is the second definition.
I can't judge whether this definition defines the answer.

Can you help me to learn more?

(Another definition for gym shoe that I've seen is " It has gripping 'soul', you might say".)

I've seen this clue in The Times and The Sunday 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.