I believe that you stated that this new air horn is replacing the existing?
If that is true, match the components up to the old air horn.
With luck, they should be near exact unless you increased the size of the unit.
Prior to starting, check that the fuse that support the old air horn is not burnt-out.Regardless remove the fuse.
If it is, check the instructions to assure that the fuse amperage is correct, if not that will need to be changed to meet the needs of the new one.
Assuming the air horns are fundamentally the same, simply remove the old and replace with the new.You should be able to use the old wiring.
Take care to inspect and disconnect the wiring. Use your phone camera to take photos, of which color wire goes to which terminal and the positioning of each part.
Assure that the black (ground wire) are cleaned, free of rust and connected properly. It is not uncommon to find that rust has developed at the connection point(s) as this in one of the most common failure points, especially on ground wires.
Install the new fuse.
Test your new air horn.
Unless you are upgrading to an air horn on an over the road truck by place a Train Air Horn, your compressed air pump should be the same size as your existing unit. Point being, this type of compressor is not high-voltage like units for suspension systems, which require direct battery connection, relays and up sized wiring.