There is the defend action - which lets you force a disadvantage upon your opponent. My Barbarian player used it to great effect in one combat... He raged then defended (at level 2) against a half dozen kobolds... while the rogues sniped at the kobolds.
And you may want to look at the "Defensive Duelist" feat. Proficient finesse weapon wielded? React to add Proficiency Bonus to AC. Sounds VERY much like a parry.
And, of course, the Battlemaster Subclass of Fighter can drop a superiority die for damage reduction using the Parry maneuver, and anyone can buy a superiority die with a feat.