At least in one major way, yes.
In 5e, to grapple someone you make a Strength (Athletics) check opposed by their Strength (Athletics) or Dexterity (Acrobatics) check, and if you win they are Grappled, meaning they cannot move, but that’s it.
So imagine your party Wizard is being attacked by a melee brute, let’s call it a Bearded Devil. You’re a big Barbarian or Fighter and want to grapple the thing to get it to lay off the Wizard. You go up and succeed the opposed check, and you’re both now Grappled.
What has changed? Almost nothing. If the BD’s turn comes between yours and the Wizard’s, the BD still gets to attack the Wizard totally unimpeded. If the Wizard’s turn comes between yours and the BD’s, then they either have to Disengage or take an opportunity attack, the same as if the BD weren’t grappled at all. The only difference is that if the Wizard disengages or eats an opportunity attack and successfully moves away, then on the BD’s next turn, it has to either attack you or use its action to try to escape the grapple to pursue the Wizard.
That is a tangential benefit that almost certainly is less useful than just hitting the thing or at least knocking it prone.
But the One D&D UA released today changes that in a good way! The new Grappled condition gives disadvantage to attacks against anyone other than your grappler. So as soon as you grapple the Bearded Devil, its opportunity attack against the fleeing Wizard is now at Disadvantage! And even if the BD’s turn comes before the Wizard’s, it has an incentive to attack you instead of the Wizard even though the Wizard is still next to it. So you instantly help out your party’s squishies by grappling the melee brute that is attacking them! Exactly how you imagine running up and engaging your companion’s assailant should help.
It’s not all good news for grapplers and bad for grapplees, though. The Bearded Devil now gets a free chance to break the grapple at the end of its turn instead of having to use its action. So if the BD’s turn is before the Wizard’s, then it will likely attack you to avoid disadvantage, and then attempt to break the grapple. If it succeeds, then the Wizard still faces a full OA when they run on their turn.
In summary, there are three ways a successful grapple changes this scenario: either 1) the Wizard is able to run away and only face an OA with disadvantage, 2) the BD attacks you instead of the Wizard, but breaks the grapple at the end of its turn and still fully threatens the Wizard, or 3) the BD attacks you instead of the Wizard and fails to break the grapple at the end of its turn, so the Wizard also only faces an OA with disadvantage.
Either way, it’s a lot better than maybe sucking up the BD’s action a whole turn later after it’s already made another round of attacks and opportunity attacks on the Wizard. I’m implementing this immediately. Three cheers for One D&D!