Robert Griffin III's PDA with Hot New Blonde

With his marriage apparently over, Robert Griffin III has already moved on ... 'cause he's getting VERY close with a smokin' hot new blonde and TMZ Sports has the pics.

Griffin is currently separated from his wife, Rebecca Liddicoat, (they have 1 child together) ... with a divorce in the works.

But over the past couple of weeks, he's been out in public with Grete Sadeiko -- a 23-year-old Estonian-born track and field athlete who currently attends Florida State University.

In fact, the two held hands on the famous Hollywood Walk of Fame during a recent trip to L.A.

There's more ... Grete has also been posting thinly-veiled messages to the Cleveland Browns QB on Twitter (as pointed out by our friends at BSO) ... even referring to him as her "baby."

On August 12th, the Browns took on the Packers in a pre-season game. Grete tweeted, "Good luck to my baby tonight!!! And then hurry home."

She included an emoji of a dog (Browns reference) and a football.