Will installing Linux clear any malware off a used laptop?

For an ordinary used laptop, a clean Linux install that replaces the whole system disk is a reasonable precaution. In the installer, look for the option to erase the disk and install Linux, rather than installing alongside the existing system.

Double-check that you have selected the right drive. Anything you need to keep on it should be backed up first, because that option removes the existing partitions and their contents from normal use. You don't need to run a separate cleaning tool beforehand.

There is a caveat: malware can theoretically persist in firmware, which a normal disk erase won't replace. That is a much less likely concern than malware on the drive, though, so I wouldn't treat it as a routine reason to avoid a used laptop.

If you have a specific reason to suspect a targeted attack, firmware inspection or reflashing may be worth considering. Comparing firmware dumps is specialized work, and differences alone don't necessarily prove there's malware.

No need to fill the drive with random data just for malware concerns. On an SSD, extra writes add wear, and erasing empty space isn't the same thing as replacing the existing installation. Use the installer's whole-disk option instead.

If the laptop has an old hard drive, replacing it with an SSD is another option. You get a fresh drive for the installation, though it costs money and doesn't address the unlikely firmware issue.