Netherdrake rep grind

Do you have to grind the rep to exalted on each toon inorder to have a netherdrake on more than one toon? And if not if you have exalted with netherwing on a horde will your ally toons be able to buy a netherdrake since you have horde with exalted? I have one toon I used to play back in BC almost got to exalted before I stop playing back in BC which this toon is ally. I now play horde and I want to finally get my netherdrake since its been a goal and my fav flying mount since BC. Can I just finish off the rep grind on the toon that I am almost exalted on or do I have to do the entire rep grind on my main toon here in shadowlands to be able to use the mount on my main.

Once you grind the rep you can then buy the Netherwing Drakes on that character. When you right click the mounts you essentially “learn” them unlocking the ability to use them on all your other characters, Horde and Alliance without restriction.

Edit: I should mention this only applies to retail. I believe Classic wow has different rules regarding rep and mounts where you would have to grind it on each individual character.