In order for your new screen to adhere properly, you'll need to thoroughly remove all of the old screen adhesive and its residue.

Use a spudger to scrape up and remove all of the old screen adhesive from the perimeter of the frame.

Once all of the old adhesive is removed, use high concentration (>90%) isopropyl alcohol and a microfiber cloth to remove any remaining adhesive residue.

Allow the alcohol to dry completely before continuing.