From what I saw over the years on many chimney crowns; any attempt of bonding new concrete to existing concrete fails sooner or later. It depends on workmanship and individual conditions / circumstances but it eventually separates, crumbles and sometimes causes more damage.
This is probably because it traps water in a seam between the old and new concrete, no matter how good this seam is, concrete is porous and absorbs moisture. If there are no cold winters in your area and ambient temperature is always above freezing, your project should definitely perform longer than if set-up in a mixed climate geographical location.
Assuming that you currently have a concrete crown / slab on top of a masonry chimney and that slab is flush with the chimney walls, you can insert an aluminum drip edge, the same type as it is used for the roof, in between the concrete and the layer of brick, stone, or cinder block beneath it.
After that, run a bead of silicon along the concrete – aluminum seam to minimize water penetration. If there’s no space to insert the drip edge, you can cut a thin channel using regular concrete blade and a circular saw.
I don’t know exactly how this chimney looks and if something like that wouldn’t compromise its appeal but it would definitely save you a lot of work, time, and probably money. Aluminum will not deteriorate either (you could also use copper for aesthetic reasons)… silicon will most likely need replacement every few years.