Is it damaged?
Broken stone, eroded/illegible inscription, broken or missing metal plate?
Stone which has delaminated would require professional treatment.
If a piece has been chipped off and would fit neatly back in place, it may be possible to use a water-based pva glue on a warm dry day to repair the milestone. Often the bits chipped off are too fragmented or simply lost and repair is not an option. The milestone must be left to carry its fresh scar.
If the milestone is broken in two, a repair is usually carried out by drilling matching holes, at least two, in each broken half and using stainless studding, builder’s resin-bonding and epoxy adhesive to join the parts together again.
If the break is very clean and the two parts are a good fit and the stone is unlikely to be hit and broken again, it may be possible to coat the two broken surfaces with water based pva adhesive and fit them back together.
It is not recommended that an eroded stone inscription (or one removed in wartime to baffle the Germans) be re-carved by an amateur. It may be regarded as part of the milestone’s history too.
A stonemason / monument mason could hand cut a new version of the eroded inscription, but would usually require the stone to be removed to his workshop. The mason may offer sand blasting as a cheaper way to recut an inscription, but this will not give the correct original profile to the lettering.
The eroded inscription can be painted on the eroded stone surface with care and give a reasonable result.