You can get dry verge systems that replace the mortar with a sort of bend over edge in plastic or tile.
Roof edge mortar repair.
Use a cold chisel and club hammer to get rid of worn out and damaged mortar.
Step 3 prepare the surface.
I would then probably coat the entire point with a waterproof seal.
Aside from the cracks the majority of the mortar is still sound and may be difficult to remove without damaging displacing the slates.
You can buy sealant in several colours to match the mortar if it is to be left unpainted.
Remove loose and worn out roofing material as well.
Repair small cracks small cracks in the mortar of the verge can be quickly and easily fixed by using a roof and gutter sealant.
By avoiding some typical mistakes you should be able to ensure that your home remains protected from the elements.
Depending on how the roofs join you may have to cut a slot to work it in far enough.
If there are repairs to be done on the roof replace worn out tiles and make sure the entire surface is covered.
This is injected into the crack with the applicator and allowed to dry before being painted over if required.
Begin by removing the shingles down to the wood sheathing and slip a strip of adhesive ice and water barrier available where roofing repair products are sold under the soffit main roof joint.
Afaik it is quite a bit of work to fit them to an existing roof but fairly easy when you are building or reroofing i have the same problem.
Concrete tile roof repair can be a very challenging process.