The theatrical release of the Re:Zero-Starting Life in Another World OAV, titled Re:Zero-Starting Life in Another World-Memory Snow, is right around the corner in Japan and according to Crunchyroll another OAV is in production.
This second OAV is titled Re:Zero-Starting Life in Another World-Hyouketsu no Kizuna (“Freezing Bonds”) and will be based on the light novel of the same name. Details are pretty scant at the moment with the cast, staff, and release date not yet announced, but the story will take place before Emilia is called to become a candidate in the king’s election and detail her first encounter with Puck.
I’m sure as soon as more information becomes available we’ll be here to let you know.