I’m quite a ‘classic (some might say boring!) dresser, and I would absolutely wear that skirt with high boots, but they’d need to be a close fitting, slim style - ideally a ‘sock boot’ or if not, a suede boot (leather would look odd) - and sit high enough up that there is no awkward gap between skirt and boot.
I like alk-black outfits with different textures of fabric involved, so I’d wear it with a long sleeve, fitted black polo neck or a boxy, possibly ‘fluffy’ sweater in black, OR a slouchy fine-kniy in dark grey or possibly a very dark brown. I think you could pull that off nicely for winter work wear.
‘No bare legs / nude tights / bare ankles showing’ after October half term was always my rule (a completely made up by ME rule, to be fair) when worked in education.
If it was Spring, I think nude tights / bare legs and trainers/high tops and a boxy jumper would look great, but maybe not for school unless you’re the ‘I’m a bit funky, me’ art teacher or summat 😉