There are areas, where you need to combine your carpeting with other coverings. example: stove. At least 50 cm on each side around a fireplace or stove, the floor covering must not be combustible, so don't be a carpet. You have to use refractory materials like steel here, use glass or tiles. The carpet itself does not have to meet any special fire protection requirements, if the distance to the fire source is maintained. Due to the relatively large temperature differences between operation and non-operation of the fireplace, however, the carpet in this area is subject to high tension, which a simple fixation with glue- or velcro or fixer would not usually go along. Ergo, you should fully glue the carpet here.
The tiles are inherently fireproof, at least in the temperature range of an average stove. However, it is advisable, Steinzeug- or to lay glazed tiles, because you have less maintenance effort when removing the very fine soot particles.
This is how you choose the size of the tile surface, that on the one hand they keep the minimum distance from the chimney to the carpet, on the other hand, no tiles have to be broken up. A small drawing will help you to determine the exact dimensions and material requirements. The transition rails must also be fire- and heat-resistant and consequently be chosen from metal. Since the covering thicknesses of tiles and carpet are certainly different, the built-in rail also needs a corresponding slope, so as not to become a stumbling block. The rail is simply inserted into the adhesive bed of the tiles, the carpet later bumped into it.
As an alternative to this solution, you can of course protect the carpet around the fireplace from flying sparks afterwards, by placing a suitably sized sheet of glass or steel on the carpet and placing the fireplace on top. However, the material thickness of the plates is so great with this load, that inevitably there is a tripping hazard at the transition to the carpet, which should be covered with metal rails. You should better just glue these splints, this protects the carpet from drilling holes. On floors with built-in underfloor heating you have to glue them anyway, drilling and screwing would be too risky. Adhesive strips are available in all possible decors.
However, this variant has the disadvantage compared to laying at ground level, that you cannot replace your carpeting without major effort, because you have to remove the chimney at the same time. The additional effort for the tiled surface would therefore pay off again at the latest with the first renovation.