Red soul shard gem will not be available in season 13. There is no way to transfer items into a season and the event will be over. Now if you are talking about the transmog, I can't rememver if it is there but thinking it should be.
If I remember correctly Red Shard Transmog is available account wide (SC/HC separated) after you unlocked it. That means you can use it even if there is no Darkening of Tristram event available.
As for the gem itself it works just like other items in the game. It will be transfered to your non-seasonal characters and will be available to loot by seasonal chars in season parallel to Darkening of Tristram.