very few places are big enough to have a dedicated QA team that can run its own agile processes. Possibly if you have SDET roles or similar and enterprise test tooling to maintain but very few can afford that. If you can then hire an expert scrum master to get you started because you need advice tailored to your situation.
I have found it far more common to be a QA placed in a scrum team, with the goal of delivering tests with functionality as part of the definition of done.
With a good scrum master, this can be a fun and productive way to be a QA, you are fully engaged and can shift left testing into the design phase.
That is not to say there aren't team activities for a QA team, its good to coordinate efforts across teams and thats a vital part of a good QA process. However, being in two scrum teams tends to undo any of the benefit as it makes for a lot of conflicts and limits the amount of time you can use in one go.
Unless you can clearly say your QA team produces products (frameworks, infrastructure, sdks) then it very likely doesn't need to use agile processes.