Kiefer Sutherland stars as John Weir in the Paramount+ series “Rabbit Hole.” (Courtesy of Paramount+)

Something just feels right about Kiefer Sutherland being in the center of a tense hourlong TV drama series.

Sutherland, of course, spent about a decade portraying Jack Bauer, a do-whatever-it-takes counter-terrorism agent who, again and again, had exactly one day to save the day in Fox’s “24.”

A veteran of movies including “Young Guns” and “Flatliners” before starring in “24,” Sutherland followed up that largely loved thrill ride by performing in other series, including ABC’s so-so “Designated Survivor.”

Now, he’s jumping into the streaming waters with the espionage thriller “Rabbit Hole,” which launches its eight-episode debut season March 26 on Paramount+.

Based on the first four episodes, which were made available for review, the solid but unspectacular “Rabbit Hole” is at times as riveting as “24” and at others almost as silly the latter could be at its low points.

That said, and as capable as Sutherland’s new character, John Weir, is, he’s not Jack Bauer.

We meet John, nervously, rapidly tapping his thumb, in a church confessional.

“Thank you for seeing me, Father,” he says. “I need help.”

Know that John isn’t looking for spiritual guidance but instead simply for someone to lend him an ear, someone who won’t repeat anything he’s told. John hasn’t slept for a few days, and, he says, he’s losing his grip on knowing what is real and what isn’t.

He used to have someone to turn to at these times, but that person is dead.

This first hour of “Rabbit Hole” then takes us back three weeks, to a confident John doing what he does best: manipulating competitors of his corporate clients into taking actions that will cause themselves harm and land him a big payday. For example, he orchestrates a nifty, technology-assisted maneuver at a restaurant frequented by Wall Street heavyweights.

To him, this kind of work is “consulting.” To Josephine “Jo” Madi (Enid Graham), an agent with the FBI who investigates financial crimes, it’s “corporate espionage.”

At the restaurant, John hits it off with a woman he encounters, Hailey Winton (Meta Golding, “Empire”), and spends the night in her hotel room. In the morning, he makes it clear he believes Hailey is working him — be it for Jo or another adversary — and says she should know blackmail won’t work because his marriage has been over for a while. Even after he unearths a hidden camera, though, she angrily insists she has no idea what he’s talking about and demands he leave.

Soon, though, John’s life begins to fall apart — after a job for a company led by a longtime friend (Jason Butler Harner) goes sideways and a murder is pinned on him — and he drags Hailey into his world, believing she’s a part of whatever is happening.

To say much more about the plot would not be best, as this is a series that wants to keep you guessing as to what is real and who actually knows what.

While it does a reasonably good job at that — at least through the season’s first half — writer-directors John Requa and Glenn Ficarra (“This Is Us,” “WeCrashed”) struggle with the shaping of Sutherland’s character. Depending on what the story demands at the moment, John may be the smartest guy in the room or a mental step or two behind the viewer.

Plus, you can’t help but wish that, as the series progresses and they must work together, that the increasingly flirtatious banter between John and Hailey generated a bit more sizzle. It’s also meant to be comedic at moments, but don’t expect to laugh out loud.

At the end of the second episode, the series introduces a character — whom we are surprised to see — portrayed by the always terrific Charles Dance, who portrayed the brilliant and ruthless Tywin on “Game of Thrones.” Dance gives the series a boost at a time when it needs it, but his character, too, isn’t as well-crafted as you’d hope.