Thick dust on my plant...

I dust it, but it came with my flat and the oldest leaves have a mm or so of thick grey dust that won’t rub off. It’s a yukka plant (I think) and the leaves are slightly sticky, I don’t want to damage the leaves by scubbing.

How can I get rid of this dust?

It is likely that this is not dust, but a naturally occuring yeast.

The dust is quite fibrous and dust-like and the same colour as fresh dust that gathers (and is removed) on the new leaves - only the old leaves are sticky though. I’ll post a photo if it helps.

If it really bugs you, cut the leaves off. A mild soapy water mix (rinsed well) won’t hurt the leaves of a yucca plant.