Your padel level updates about an hour after the match score is confirmed. The next time you open the app, you'll see "Your new level is" with your new level.
What happens after your match
When the match ends, every player gets a notification: "Report the score from your recently played match".
One player reports the score. Only one is needed.
The other team gets a notification: "Confirm the score that was reported from your match".
One player from the other team confirms it. If nobody confirms or disputes within 4 hours, the score is confirmed automatically.
About an hour after the score is confirmed, levels are updated.
Why does it take an hour?
So that every player has time to give feedback on the others' levels, not only the players who reported and confirmed.
Good to know
There's no notification when your level changes. You see it in the app, on your Profile tab.
If the score is disputed, levels only update once the club resolves it. See "How do I confirm or dispute a reported score?".
Tennis scores are recorded but don't change your level.