As we know selenium is just a browser automation tool. Selenium Grid will help you invoke multiple browsers and controle those using your code at the same time.
TestNG is testing framework which you use with Selenium WebDriver to manage your automated test suite.
At this point of time, I can think of JUnit 5 with Maven's maven-surefire-plugin. By configuring maven-surefire-plugin you can execute JUnit test cases in parallel.
Hope that helps.