How can this image be turned white - the figures, clock etc, so that it can be placed on a black background, while still retaining its quality?
One thing to try is a fake metallization trick. It should be done differently to the clock and to the statue figures, but I made a compromise because your attached image has too low quality for easy separation. I guess you have them separately.
First I made (a complex) selection and deleted the white background with it. Layer mask doesn't work here, the BG must be fully transparent, but the white parts in the clock and statue shapes must stay intact. I desaturated and duplicated the remnants of the original and inserted a new black background:
The upper copy got a curves layer (next layer only switch=ON) which simulates solarization:
The result is a little greyish due the ridiculously uncontrollable curve tool of Photoshop. It's practically impossible to adjust it right. The greyness will be fixed later.
The curve doesn't affect to the clock in the right way because there's no right contrast in the right place. That's worked around by inserting layer style Bevel&Emboss > Outer bevel to the lower copy. It generates the wanted light edges. Unfortunately it adds an edge to the statue shapes, too. A good edge to the clock can be too much for the statue figures. That's why they should be separate. I tried to find a compromise.
The greyness can be fixed by inserting a curves layer above all. No layer grouping is needed, because the new curve doesn't lift black:
ADD: Just found your earlier question which had a little better quality statue figures altough still very noisy ones. The next zoomed view shows how bad the image is:
There's no hope of glossy result. There are noise reduction plugins for Photoshop which quite cleverly guess which details are noise and which should be saved. I used Redfield Perfectum for this:
I'm sure advanced Photoshop users get the same without plugins, but I used one to avoid experimenting.
The fake metallization result is clearly more polished now:
Your own attempt in your comment has very coarse clock image which isn't even unsaturated (it has colored noise) and the outer bevel is far too wide. It obscures the text. For perfect result I would redraw the clock and texts in Illustrator.
From what I understand, you want to turn the image white and the background black. One method could be using a negative filter and manually refining the color values.
I think that you need to redraw it completely. But if that is not possible maybe just increase the brightness or something in software like Photoshop or something familiar. When doing this, make sure it is a transparent PNG.