Hi lauriel50178684,
If you're referring to an Acrobat.com online subscription, you can simply log on to https://cloud.acrobat.com via a web browser on your new computer.
If you purchased an Acrobat subscription, you can redownload that from https://cloud.acrobat.com/acrobat. This pages offers some great step-by-step instructions for downloading and installing an Acrobat subscription: Acrobat XI Subscription | Download and install
Best,
Sara