Pretty kitchen from what I can see! I agree that mirror is rather strange in that location. It almost seems like a window should be there but....I wonder if maybe some artwork might work there? Trying to visualize if backsplash were expanded to it but I don't think that would work....I am looking forward to seeing what others suggest because I am not so creative.

I don't know what other colors you have in the room, but maybe paint it a color to accent it and hang artwork there? See I really am not too swift at this but really want to hear suggestions too!

Without seeing the whole room, it's hard to say, but I might want to paint it the same wall colour, but put shallow shelves there -- you could put plants there if you have a green thumb. Or you could make the shelves into a drying rack (if you do hand washing of small items like knives or coffee mugs (I know some people would find that aesthetically appalling, but it would suit me well). Or, if you use the mirror to watch over your shoulder while at the sink, at least put up a more decorative mirror in a nice frame.

Or a plate rack,

The plate rack is the only option which will be used for washing kitchen crockeries.

I don't know for what reason your previous landlord has put that mirror in the kitchen. They might have hide something behind it be careful (Jokes apart).

You can leave it, add another cabinet, add shelves, art

shelves, but... the first one will have to be very narrow, as it has to be very low and sit on top of the tile lip. thats ok, just choose a style that comes in very narrow and then regular narrow.

you can mock this up with varying strips of cardboard, and see how small it has to be to not whack it with a roaster pan you are hand washing.

if it turns out that NO shelf is small enough to be that low and not make you crazy, switch this mirror either for art or a more decorative style of mirror.