How to remove an Apple ID from lap top to a new Apple ID

It depends on what you mean by cancelled. If the Apple ID is cancelled using Apple's definition - see How to delete your Apple ID account - Apple Support - then it is likely that you will not be able to sign out of the Apple ID account.

Apple specifically advises in this document:

• Make sure that you sign out of all your devices to avoid issues with apps that use your Apple ID account or iCloud. After your account is deleted, you can't sign out of iCloud or turn off Find My iPhone Activation Lock on your devices. If you forget to sign out, you might not be able to use your device when your account is deleted.

To sign in to your iCloud services on the device you first will have to sign out using the password of the Apple ID it is using currently.

Once you have signed out of that account, sign in using your own Apple ID credentials. Follow the instructions in Apple's document Sign in with your Apple ID - Apple Support