Chris Pine is apparently Paramount’s chosen reboot specialist. After reviving James Kirk in the new “Star Trek” franchise, he now takes on the task of resurrecting Jack Ryan, the government agent created by Tom Clancy who was previously played by Alec Baldwin, Harrison Ford and Ben Affleck. Again he does a pretty good job of making the character his own, just as he did with the captain of the Enterprise. And “Jack Ryan: Shadow Recruit” proves a surprisingly decent showcase for him. Like “Star Trek” it’s a prequel, a “Ryan Origins” episode. But though updated to the post-9/11 present, it’s a pleasingly old-fashioned piece, reminiscent of “Mission Impossible”—and not the Tom Cruise movies but the CBS series they were based on.

Ryan’s introduced here as a economics grad student who joins the Marines when 9/11 hits, serving in Afghanistan, where he’s severely injured when his helicopter’s brought down by enemy fire. During a long stint in rehab he connects with his demanding nurse-therapist Cathy Muller (Keira Knightley) and is approached by soft-spoken William Harper (Kevin Costner) to join the CIA as an analyst working undercover on Wall Street to uncover transactions that might point to terrorist connections.

Ten years later, Ryan—who’s finished his interrupted PhD—is ensconced in a big New York firm and a committed relationship with Cathy, his live-in girlfriend (and now a doctor herself). His scrutiny of orders involving a big Russian outfit headed by Viktor Cherevin (Kenneth Branagh) reveals some discomforting anomalies that he passes on to Harper. His analysis is that Cherevin intends to amass a huge stack of US treasury bills and then dump them on the market, leading to a worldwide panic that will collapse the dollar and bring about a second Great Depression. But he also predicts that in order to work the scheme, which has probably been set in motion as retaliation for US support of a Turkish pipeline that will negatively impact oil prices (and thus Russia’s financial security), will also simultaneously require a major terrorist assault in America.

Jack’s dire assessment leads Harper to send him posthaste to Moscow, ostensibly to do a thorough audit of Cherevin’s books on behalf of his brokerage. But when Cherevin deflects the audit (apparently after arranging a hit on Ryan that the American foils—which makes for an exciting fight sequence but, in retrospect, seems unnecessary given that he’s already derailed the investigation), Jack’s enlisted to break into the Russian’s office and purloin his files. The caper is complicated by the arrival of Cathy, who’s become suspicious of her fiance’s secretiveness but immediately becomes part of an elaborate, though dangerous, plan to secure the records by outsmarting the place’s massive security. This Moscow narrative thread dovetails with the American side of affairs, which involves the awakening of a determined Russian sleeper agent who’s the linchpin of Cherevin’s plan to shake the very foundations of the US economic system.

If one were to jettison the elements that put this story into a contemporary setting—the aftermath of 9/11, the transformation of Russia into a corrupt “capitalist” system dependent on her oil reserves for survival—you could easily imagine this as a period piece set in Soviet times, with Peter Graves, Martin Landau and the others of their team doing their best to foil a dastardly plot concocted by KGB officials. But “Shadow Recruit” demonstrates that the old formulas are still pretty potent, especially when they’re directed with aplomb by Branagh (who understandably took the juiciest role himself), nicely shot by Haris Zambarloukos and skillfully edited by Martin Walsh (who manages to keep the action intelligible, especially in the Moscow sequences, although he’s hampered by a damsel-in-distress car chase there, and then has to smudge over the implausibility of the later scenes in America in which Ryan brilliantly figures out the specifics of the terrorist plot). Patrick Doyle’s score gives the action a propulsive push, too.

Sometimes, to be sure, the moth-eaten clichés become a bit much. Surely the scene in which Ryan passes along material to an agency courier in a revival movie theatre is intended as a wink-wink moment. The damsel-in-distress thread involving Cathy and Viktor in the Moscow sequence has a musty feel. The last reel, in which the terrorist attack on US soil is averted at the last moment (the sort of conclusion of which Clancy would have generally approved, even if he probably would have liked a lot more military hardware like missiles and submarines to be involved), disappoints simply because it’s something we’ve seen before. (In fact, there was a recent network TV show in which the method of disposing of a bomb was precisely the same.) And the final scene in Washington is pretty juvenile.

Still, one’s willing to overlook all of this not only because the picture is so technically accomplished, but because the cast is so winning. The handsome but agreeably vulnerable Pine again demonstrates that he has the makings of a real movie star, and Knightley comes across surprisingly strongly, given her disappointing recent work. Costner, who’s lately been similarly aimless (with the exception of the underappreciated “Mr. Brooks”), brings a nicely understated, no-frills attitude to Ryan’s mentor, and Branagh showcases his sadistic, simmering side as the driven Russian patriot inspired by a painting of the defeated Napoleon on his office wall.

“Jack Ryan” doesn’t have the pizzazz of a James Bond extravaganza, or the dark excitement of the better Jason Bourne films (the ones with Damon, that is, not Renner). But it manages to deliver a couple of hours of cheekily retro, amusingly implausible spycraft.