You mean curb? I would first roughen the old concrete surface to provide something for the new concrete to adhere to.
Get some #3 rebar and cut it into 8" or so lengths, drill holes about 18" apart in the old concrete about 1/8"diameter bigger than the #3 rebar.
Make sure you leave at least 2" from the bottom of the existing concrete when you drill the hole.
IE if the exist concrete is 6" thick, only drill 4" down.
Also, leave 2" cover of concrete above the top of the vertical #3 bars glued into the exist slab. IE, 6" curb, leave 4" sticking out of the existing concrete.
Fill the holes with concrete epoxy such as Ramset C6 fast cure or Hilti. Stick the 8" long rebar into the holes and wait about an hour to cure with a fast setting epoxy like the C6.
Tie one continuous #3 rebar at the top of the vertical rebars glued into the the existing concrete.
That should help.