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If history has taught us anything, it’s that no one is truly safe. This gathering fear fueled some great 1970s paranoid thrillers like “Parallax View” and “The Conversation,” but it’s hard to replicate the dangers of today’s ultra-online world, where our devices explain and indulge with abandon, conspiracies are the lifeblood, and we feel stalked one day, invisibly anonymous the next.

The premise of “Relay,” the new white-knuckle thriller from “Hell or High Water” director David McKenzie, is that a certain kind of tech-savvy hero can, if not completely ease your anxiety, at least navigate a secretive path with those who get you. And Riz Ahmed’s lone off-grid fixer, Ash, who hides in plain sight in bustling New York City, can do so without ever meeting or speaking to you: His preferred mode of tracking communication is a text-to-phone service that hard-of-hearing people use in conjunction with message-prevention operators. Like a ready-made covert operation, it keeps identities, numbers, and call logs secret.

For the simple fact that “The Relay” doesn’t involve a hitman (the film’s most romanticized independent contractor), screenwriter Justin Piasecki’s script deserves kudos. Rather, Ash’s broker helps would-be whistleblowers escape the clutches of dangerously far-fetched entities—unless, of course, they’re willing to part with the cash. It’s a fascinatingly cynical update: Should we make an uneasy peace with our tormentors? (Hello, today’s headlines.)

Before these questions are answered, however, the “relay” has set up with the precision of a clockwork, a simple big-city nail-biter about staying one step ahead. Seeking protection from harassment and a return to normal life, rattled biotech scientist Sarah (Lily James) continues to handle incriminating documents about her former employer. When she’s rejected by a high-powered law firm, she’s provided with a mysterious number to call. Ash, armed with his sophisticated vetting methods, puts Sarah through PacES with rules and instructions for burner phones, mail-in packages, and a detailed itinerary for seemingly random air travel. But it’s not just her determination that’s tested—it’s also a ploy to outwit the corporate goons on her trail: a dog-sniffing team led by Sam Worthington (who should probably only play bad guys) and Will Fitzgerald.

As the story careens through airports and post offices and the back alleys of New York, the cat-and-mouse chase is a dizzyingly enjoyable one, worthy of a Thomas Perry novel. We expect mistakes that threaten everything, of course, and they begin with the learning that Ash himself is a failed informant who begins to question his chosen crusade. Another vulnerability, recognizable in the occasional cracks in Ahmed’s commanding stoicism, is the loneliness of the gig. So when RESIVE SARAH, on one of their protected calls, gently teases out a smidgen of personality from her mysterious unseen assistant, one is inclined to shout, “No feelings! Too risky!”

But it’s the slippery joy of “The Relay,” of course, that propels individuals toward venal institutional grandeur. The downsides are the beating hearts of these films, the danger that makes the blood pump faster. Some of that effectiveness is down to a few musical choices, but McKenzie’s command of the material is solid, Giles Nuttgen’s cinematography achieves a smooth, moody metallic chill, and Matt Mayer’s editing is always fleet. In a year that has already given us one adult Peekaboo—Steven Soderbergh’s “Black Bag”—“The Relay” proves that there’s still room for more clever, subtle plaster-and-dagger possibilities.