Post-Imperial Age is a possible setting for the starting Age in random map and multiplayer games in Age of Empires II and Age of Empires III. It is not an Age by definition as it is not possible to advance to it through research. Rather, the term refers to a player starting in the Imperial Age with all technologies that are available to their civilization already researched.
In Age of Empires III, all Home City Cards that are placed in a player's deck will be available instantly, as in Post-Imperial, the player has already reached the Industrial Age.
Unfortunately, games that start in the Post-Imperial-Age do not allow players to re-use cards, as with ones before the Imperial. In normal games, players who advance to the Imperial Age can utilize any unit cards that have already been shipped one more time. For example, if a shipment of three Settlers had already been sent e.g. in the Fortress Age, anyone who has reached the Imperial Age might send this one more time.