One of the new features coming in Season 3 are Vaults, a new type of dungeon where you fight against the Constructs with various traps scattered throughout. Blizzard has stated in their Developer Update Livestream that players will be able to level their Paragon Glyphs in the Nightmare version of Vaults.
Season 3 Developer Update Livestream Summary Diablo 4 Season 3 Overview
After completing a Nightmare Vault, players will be able to upgrade their Paragon Glyphs in a similar way to Nightmare Dungeons.