It might be old plastic, or Bakelite, but I think it’s horn. Question is, what can be done to freshen up, blacken, an old buttplate that’s gone brown?
Spirit shoe dye works well on Horn because in its way it is slightly porous so it absorbs the dye colour. Plastics like Bakelite and others are not absorbent in any effective way so it will have to be a surface preparation. Black wax boot polish is better than nothing on these types of plastic, though some spirit coloured Lacquers can give good results but like wax polish ware removes them, so it is a repeat process.