A town hall in Iowa on Wednesday is the network’s first live interview with the former president in nearly two years, the latest twist in a long-running drama.One of television’s longest-running soap operas is about to start a new chapter.Donald J. Trump has not appeared for a live interview on Fox News since April 2022, a nearly two-year stretch of chilliness between the former president and the channel whose airwaves he once relied on to cement his status atop the American right.In that period, all of Mr. Trump’s Fox News interviews were pretaped, a notable precaution for a network that paid $787.5 million to settle a defamation lawsuit fueled by the former president’s mendacious claims about the 2020 election. That changes on Wednesday, when Mr. Trump will appear live on the network for a town hall in Des Moines ahead of the Iowa caucuses.The relationship between Mr. Trump and the Rupert Murdoch-owned network has featured more drama than a season of “Real Housewives.” But Wednesday’s event is not only a turning point and a potential ratings winner for Fox News: It is also the former president’s first live interview on any major news network since he went on CNN last May, an event that drew harsh criticism for the volume and velocity of his unfiltered false claims.Mr. Trump has not exactly been silenced. He refused the invitations of several networks to participate in live Republican primary debates. And he has agreed to numerous pretaped interviews, including an appearance on NBC in September that also prompted complaints from viewers who berated the network for providing him a platform.His relationship with Fox News, however, is especially complicated. In fact, it wasn’t that long ago when parts of the network seemed to be moving on.Back in 2022, Fox News snubbed Mr. Trump’s rallies while offering admiring coverage to a rival, Gov. Ron DeSantis of Florida. After Mr. Trump announced in November 2022 that he would again run for president, the network kept him off its airwaves for a full five months. When Mr. Trump did return, for a taped interview last March with Sean Hannity, he received a cool reception from other Fox hosts; one network contributor called his appearance “absolutely horrific.”The slights angered Mr. Trump, who has harbored resentment toward Fox over its early projection of Arizona for Joseph R. Biden Jr. on election night in 2020. Over the past year, the former president has lobbed crude insults at Mr. Murdoch and denounced Fox as “fake news” and “hostile” in posts on Truth Social, his preferred social media platform. He has also grumbled to allies that the network erred in settling the defamation suit brought by Dominion Voting Systems, saying it offered ammunition to other potential litigants.In an interview, Bret Baier, Fox News’s chief political anchor, who is moderating the Wednesday event alongside the anchor Martha MacCallum, did not shy away from acknowledging the volatility of the relationship.“We’re one Truth Social post away from some different feeling,” he said.Despite the wariness, both sides found reasons to agree to Wednesday’s town hall.Judging by his poll numbers, many conservatives remain enthralled by Mr. Trump, and keeping the potential Republican nominee at arm’s length would erode Fox News’s credibility with a core audience. While Mr. Trump has told confidants that he believes Fox News has lost some influence with Republican voters, it remains the highest-rated cable network and home to influential conservatives like Mr. Hannity and Jesse Watters.Furthermore, the town hall gives Mr. Trump a chance to dunk on both his presidential rivals and one of his media bêtes noires: CNN.CNN had previously announced that it would sponsor a Republican debate in Iowa on the same night, in the same city, at the same time (9 p.m. Eastern). Mr. DeSantis and Nikki Haley, Mr. Trump’s closest rivals in state polls, will be at that debate, but Mr. Trump boycotted. Fox’s town hall allows him to siphon away attention and potentially deliver a TV ratings victory over CNN — which would also please Fox News.Given the rough-and-tumble nature of a presidential campaign, Wednesday’s telecast is unlikely to represent a lasting détente. One person with direct knowledge of interactions between the Trump camp and Fox News, who spoke on the condition of anonymity, said the relationship remained chilly.The televisions on Mr. Trump’s plane once constantly aired Fox News, but that is no longer the case, the person said. The former president often requests to watch Mr. Hannity’s program, but sometimes prefers Newsmax, particularly its host Greg Kelly, an old acquaintance from New York political circles. Mr. Trump remains a fan of Mr. Hannity — and of Mr. Watters and Maria Bartiromo — but he has soured on the “Fox & Friends” host Steve Doocy, whom he recently described as “not nice like he should be.”Mr. Baier said he had studiously courted Mr. Trump in recent weeks, pitching him on the idea of a town hall over the phone and at least once in person at his Florida mansion, Mar-a-Lago.“It’s not easy,” he said of the efforts required to coax Mr. Trump into an interview. He said he had encouraged the former president to take “tough but fair” questions in a live setting.“This is getting to the playoffs,” Mr. Baier said. “This is a time when voters need to see him live, in person, when it happens.”So what happens if Mr. Trump repeats on live TV his baseless claim that the 2020 election was rigged?“We’re ready to deal with it,” Mr. Baier said, noting that he disputed Mr. Trump’s claims when the subject arose at their pretaped interview last June. “But if he’s spending all of his town hall time dealing with 2020, and not talking about what he wants to do as president, he’s got other issues.” (At the time, Mr. Trump was not thrilled about Mr. Baier’s real-time fact-checking, calling it “nasty.”)For Mr. Baier, the next person on his list for a live, unfiltered interview is President Biden. “We’ve had a request in every two weeks since South Carolina, when candidate Joe Biden won the primary,” he said. “We would love to do a town hall with the president. We would do that in a heartbeat.”Jonathan Swan More