Create a support ticket inside of Stripe and explain that you wish to export your customer card information over to your new payment gateway. A good resource from Stripe's documentation is here,
To do this securely, Stripe prepares an encrypted JSON export file containing your data, including the card details of your customers, email addresses, and any attached metadata.
Thought needs to be given to the timing of the secure transfer with your new processor, who uses this file to import the data into their system. You can start the migration process by contacting Stripe with the name of your new payment processor.