Your employment agreement will be with the local entity of Remote where you reside. For example, if you are based in the United Kingdom your employment contract will be with Remote's UK entity.
Remote employs you locally as the employer of record (EOR) on behalf of the company you work for. This also means that your employment agreement will be with Remote. All the business operations and day-to-day of your work is handled by the company you work for. In order to do this, Remote takes on all of the responsibilities, obligations, and tasks related to your employment.