Hi m-gigi.
welcome to this Apple (user-to-user) Community.
Re: Guided access slow and laggy
Sorry there have been no replies to your post so far.
Some games may use a lot of memory / storage space while you play them.
You could check you have enough memory / storage space free for whatever game you are playing.
Go to Settings > General > [Device] Storage, to see a bar showing used and unused space
More info: How to check the storage on your iPhone and iPad - Apple Support
If you still need help, and haven't already done so:
you may want to try updating your iPad to the recently released iPadOS version, to see if that helps:
Or, if already updated, try: restarting your iPad (deletes temporary files, re-establishes connections,
may update recent setting changes, and often restores order if something is not working as expected.
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Also: With a brand new iPad: You can get help from the hardware and software experts at Apple:
One stop for technical support, Apple hardware service, and software support.
Call Apple Support at 1-800-APLCARE (or use the app)
AppleCare Products - Apple