Each service in your catalog has a defined set of responders (who gets paged) and stakeholders (who gets notified). You set these once on the service, then pick the whole service anywhere you'd otherwise choose responders or email recipients — instead of rebuilding the same list of teams and people each time.
Go to Settings > Configuration > Services to manage your services catalog
Open a service from your Services catalog and go to its Responders tab. Use Add teams and Add users to list who owns the service. Whenever the service is added as a responder or paged, each team is notified through its own escalation policy and each user through their own notification policy.

You can now pick a whole service as a responder, right where you already choose teams and members — when declaring an incident, in an incident template, or in the manual Page dialog. Selecting a service adds and pages its responders and records the service on the incident.

In an incident template, the template points at the service itself, not a frozen list of today's responders. Declare an incident from it later, and it uses whoever the service's responders are at that moment — shown in the editor as "Uses the service's responders as configured when an incident is created."

When you're declaring an incident or paging manually, you can expand a service to see its teams and members, and skip individuals for that incident only — the service definition is untouched.

This is an addition to responder selection — Teams and Members behave exactly as before.
Open the service's Stakeholders tab and build the notify list two ways — mix both as needed:
is one of or is not one of), and Select labels to match against. Anyone whose labels satisfy the rule is a stakeholder, and membership updates itself as labels change.