HPV detection

Read lots on HPV but it’s unclear whether the test for women can actually detect if you carry HPV when there is no symptom/infection...

So when a test is clear, is it possible that you may have dormant HPV that has not yet caused any problems and thus has escaped detection?

And if it caused an infection/cells/warts before, and then you later get a clean test, people are saying that their body cleared it...but is it still there and can you still spread it?

Just confused because there’s also no cure, so not sure if that means you actually carry the virus rest of your life...in which case, it would be responsible to always inform partners. Or is there some point when it’s cleared such that you would not infect future partners?