PrestaShop enables you to give your customers certain privileges, by assigning them to groups. You can create as many customer groups as needed, and assign a customer to as many groups as you like.
Shop Parameters>Customer Settings>Groups

The discount you want to set for the members of this group applies to all products in your shop

You may prefer to not set any discount value here, and instead create cart rules.

Once these settings are in place, you can save the group as is, or add per-category and/or per-module settings. In the latter case, after the group has been saved, open it again: the form will load with two more options:

Category discount. Click on the “Add a category discount” to bring up a new window, which contains a list of all your categories. You can pick one, and apply a specific discount which will apply for that group of customers only, and to that category only.

Note that:

Only products which have this category as their default category will be affected by the discount. Products which have this category as a secondary category will not be affected.

This category discount will replace any other discount that members of this group would otherwise enjoy on this category.

You can add as many category discounts for this customer group as you need – thereby giving this group a completely different set of discounts from other customers if you need to.