Major city has short program for capturing waste (5)

I believe the answer is:

nappy

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

'capturing waste' is the definition.
I can't judge whether this defines the answer.

'major city has short program' is the wordplay.
'major city' becomes 'NY' (New York).
'has' is an insertion indicator.
'short program' becomes 'app' (type of computer program. I am not sure about the 'short' bit.).
'ny' going around 'app' is 'NAPPY'.

'for' acts as a link.

Can you help me to learn more?

(Other definitions for nappy that I've seen before include "Baby wear" , "One pinned on baby" , "Pad for baby" , "Item for baby" , "Baseball fielder" .)

I've seen this clue in The Irish 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.