Easy Anti Cheat is a required component of New World, and yes it's safe.

Is Easy Anti-Cheat safe to install?

It's no less safe than installing and running the game it came with. Not if you're a cheater. It does some low-level driver stuff that has caused a few issues in the past, but it usually does not cause problems.

Does Easy Anti-Cheat do anything?

Easy Anti Cheat (EAC) is high-tech software developed by Epic games that tries to prevent such malpractices and ban the players who use it. It's the leading anti-cheat service that runs in the background, tracking and countering hacking in multiplayer games through hybrid anti-cheat mechanisms.