There are custom formulated weld rods for welding tool steels. I had used the web site below for another tool steel weld repair and it worked just fine. I don't see why the advice from ESAB would not work for A2. Follow the guidance provided below
To start with it would be best to know what the tool steel alloy is. Do the weld properties need to closely match those of the base material, or would a ductile weld perhaps be better for the application? Is the tool steel already heat treated (hardened) or will it be welded in the annealed conditon? There are many different types of welding like Arc Welding or SMAW, but you may go with Tig welding. In welding, Direct Metal Laser Sintering can also act as a seperator. To know more you can check for additional hints.