Amber Heard isn't taking any chances ... she's got a beefy bodyguard to protect her now!

We're not sure if this new interest in security has anything to do with her abuse charges against estranged hubby Johnny Depp or if she's just trying to look VIP as she walks through LAX, but these two looked tight! And by tight, we mean surprisingly comfortable and touchy-feely close for a bodyguard-starlet situation!

This comes a day after a new report claims the two got into a NASTY fight just before they split, when Johnny suspected Amber had been unfaithful. E! News reports: "Johnny had a night out and Amber had a feeling he had been with someone. She questioned him about it and he blew up at her, got in her face yelling, chased her upstairs. Amber was scared," a source said. The source said Depp didn't admit to anything, but apologized and that Heard "ultimately forgave him."

Despite the reported feud, Depp and Heard seem to want to settle their differences out of court -- in a more amicable way ... that would certainly involved a large check being written to Heard! Last week's restraining order hearing was cancelled, fueling rumors the two were on their way to a mediation -- which MIGHT have been what Amber was doing in London. Johnny's band, Hollywood Vampires, has been touring in Europe so the two could have met up in Ol' Blightly to sign some papers. Hmmm ... maybe that's why Amber looks satisfied in our EXCLUSIVE photos of her Wednesday night at the airport?