Board Thread:DC's Legends of Tomorrow discussions/@comment-9346948-20170405000405/@comment-26537965-20170408095933

Stryzzar wrote: Though main reason I don't think this is the last we'll see of Eobard is he's Barry's arch-enemy. His complete antithesis who needs to appear at least once per season to menace Barry, much like Malcolm for Oliver.

There's also the fact, there should still be a time remnant of him in the future who needs to become enemies with Barry in the first place, become Harrison Wells and cause all of season 1 to happen.

My money is on something happens to prevent Eddie from killing himself, thereby removing Eobard's time remnant status entirely. His younger version, who does not know, who The Flash is  will probably appear again in Season 4, but I think Eobard will stay dead.