If the president is impeached and removed from office, does the VP take his place?

This Q is regarding the succession laws in the USA.

I know if the president dies or became incapacitated in some way the VP is next in line. What I’m not sure about is if the president is found with wrongdoing if that’s still the case. Even if it isn’t the case automatically, what if the VP was part of the scams and misconduct that ousted the president, then does the VP become automatically ineligible to be sworn in? Or, he takes the office and you would need a whole separate impeachment?

This is not about Trump specifically, it’s just about how the process works.