How long does Essedum's effect last?
The card has an action dice symbol in the upper right.  This means that it takes one dice to activate the card and it is only in effect while it has a dice.  I'm not sure why you say "Cards played later are not affected".  For example, the Turris does not require a dice to be active, so it adds 1 to the defense of all the player's face-up cards for as long as it is in play, whether they were played before or after the Turris.