Solutions Partners and Providers do not need to purchase any paid seats in a client's account. Historically, in order for a partner employee to gain free access to a client's Sales or Service Hub specific functionality (eg. documents, playbooks, sequences) they had to fill out a form on this page, which then resulted in a delay for you getting access to the tools in your client's account that you need.

We now have Client Access Manager, which is a new interface in Partner Tools that helps Partners manage their access to Client accounts. Client Access Manager also gives Partner Admins the ability to update the permissions of an existing Partner employee in a Client account, by selecting a new HubSpot default permission set which will be applied in the Client’s account at once.

Client Access Manager works for both legacy pricing customer accounts as well as the new seats-based pricing customer accounts. One nuance is that customer accounts who are on seats-based pricing, will have access to the new Partner Seat assignment, which further allows partner employees to access client accounts without having to pay for a seat.

If you're trying to gain access to a client account that is on legacy pricing (not seats-based pricing), then you will NOT have access to a Partner Seat, since the concept of seats doesn't exist on legacy accounts. You'll still be able to access all the functionality you need in legacy accounts by using the Client Access Manager and permission sets. 

If you're trying to gain access to a client account that is on seats-based pricing, then you'll have access to the Partner Seat assignment along with partner permission sets that give you access to everything you need.