The last mention of Edmure was in Season 3 episode 10 "Mhysa".
Look at us now, Tully. You're dead, your daughter's dead, your grandson's dead, your son spent his wedding night in a dungeon and I'm Lord of Riverrun. -Walder Frey
There has been no further mention of him, or Blackfish, or the Tullys at all in following seasons of the show, which have departed from following the books closely.
In the books A Storm of Swords match Season 3's treatment of Edmure. The following book, A Feast of Crows, has Edmure as a prisoner, used as a bait for the remaining Tullys, then given an ultimatum to turn over Riverrun, or have it and his to-be-born child destroyed. He turns it over, and now lives as a slave/vassal of the Lannisters.