Get a carpenter to make you a cover to put over it. You could have MDF and paint it to modernise it.

To put over the iron mask, or to replace the mask with the wood cover?

In my opinion, you could possibly get it repainted in a burnished steel colour and reduce the heath by at least a half or replace it with a smaller white granite / marble style to modernise. The firplace seems very dark and the hearth far too big. Alternatively remove the fireplace and hearth and put in a modern bioethanol fire using the recess.

We want to refurbish the entire living, and the starting point is the fireplace, as is the central point. I'm considering couple of options. Replacing it completely with a marble one, but is a bit pricey, and might be too traditional for our taste.
Second choise would be to install only a fireplace, an electric modern one, without the surrounding. This leaves the option of placing tv above too.

Any other options that I might consider?

I wouldn't remove it altogether, Daisy E's suggestion to have a cover made to go over the wood will give a flat modern look is worth considering. Certainly the hearth is dominating so reducing it's width and maybe a lighter color will reduce it's impact on a new room.

Please don't remove it, take away that hearth that's wrong lighten the colour try sandblasting it.

I'm afraid I don't understand what do you mean by taking away the heart. It seems to be one piece cast, around then central burner.

Oh, the marble board from below. :). Well, What I don't like the most is the fireplace cast, that is too black. I would like something lighter.

In addition, I don't thik we'll ever use a coal/wood fireplace. I like the bioethanol fireplace idea, seems to be much easier to use.

Yes, the hearth is too big and the surround too dark. It would be a shame to loose an original feature, so try painting the surround a lighter colour, assuming it's wooden. Would a gas inset fire be an option?

Some inspiration https://www.swoonworthy.co.uk/2019/03/victorian-fireplace-refresh-update.html/

I think if you painted it white it would transform the surround. However, as others have said the hearth is too big. I would cut the hearth in half length ways and I think it will look more in proportion. I think it has great potential.

It is a lovely fireplace. If yours is a Victorian house and it is an original fireplace I would not remove it. It is part of the character and history of the house. Others would appreciate it when you come to sell even if you don’t. Cover it without causing damage if you must. If not original then go ahead, remove it and sell it.