In the basic set there is an NPC, a fighter, who has a Parry reaction that lets him roll 1d6 and reduce damage. I also remember seeing the parry power/action in some beta rules.
I don’t (yet) have the PHB—is there something like that? A feat maybe?
I’ve always liked the idea of parry being for all characters, not just a fighter thing, but I want to know the official rules.
Yes, there is a feat (Martial Adept) that any character can take, which allows you to take two combat maneuvers and gain one superiority die. If the character is not a Battlemaster Fighter, they will not have other superiority dice, in which case the one they gain is a d6.
One of those combat maneuvers is parry:
When another creature damages you with a melee attack, you can use your reaction and expend one superiority die to reduce the damage by the number you roll on your superiority die + your Dexterity modifier.