Endeavour regularly opens with staccato clips of murder interspersed with our characters. Still, the opening of Season 7 uses it effectively, unveiling the Thursdays in Oxford while Morse is far away in Venice, while Strange runs the desk this New Year's Eve.
Morse is watching opera and landing in bed with fellow attendee Violetta Talenti (Stephanie Leonidas), and Fred and Win are enjoying chicken-in-a-baskets. While they do, a pair of waitresses, Molly Andrews (Lucy Farrar) and Jenny Tate (Holli Dempsey), work their way through the holiday, Molly harassed by drunk boyfriend, Carl Sturgis (Sam Ferriday) and Jenny watched by boss Tony Jakobssen (Oliver Boot). Both leave after the clock's rung, but only one makes it home alive.
Morse: What is it you're hoping to be liberated from exactly? Just the dishes or light housekeeping in general?
Frazil: Patriarchial hegemony in the main, freedom from the tyranny of the squeezy bottle's just an adjunct.
With Morse on vacation, it's up to Thursday and Strange to deal with Molly Andrews' body. DeBryn says her neck was broken, and her purse was stolen. Dorothy Frazil pops by to get the story, as to cops walk the towpath looking for possible witnesses, including a whistler heard nearby. Thursday notes Carl was tossed from the pub for drunken behavior, and he admits they were having a row because he heard she was dating someone else. Thursday's convinced Carl did it but can't pin it, and the case stalls out.
The 1970s saw a new push in the UK towards using television as an educational tool. The current program being cast out of Oxford is "Higher Mathematics," with Dr. Dai Ferman (Richard Harrington), Dr. Jeremy Kreitsek (Reece Ritchie), and Professor Blish (Angus Wright) auditioning. They are beaten out by Dr. Naomi Benford (Naomi Battrick), much to Ferman's displeasure. They're all members of the same team, in the Department of Latent Potential, and Benford tells Blish she is concerned they've been withholding something about the Andrews case. Even more concerning, the whistler is someone in her office and seems to be Dr. Jeremy.
By spring, the towpath starts to get a bad rap, with a flasher on the loose, so Bright has Morse take a second look. After speaking to Sturgis and Molly's grandmother, Mrs. Carlin (Beverley Klein), Morse flags a boat, the Rosie Jugg, passing through the canal; the driver had a history of petty thievery. At an Oxford function, Morse gets his wallet stolen. To make up for it, the organizer, Ludo Talenti (Ryan Gage), takes him to supper. It's the beginning of a new friendship when Ludo drops by to drink wine. He sees the photos of Andrews and recognizes the marks on her neck as a torn-off necklace, something he'd seen before as a child during WWII.
Benford calls the station, where Morse answers. He tracks her down at Oxford, where she's running the ERA meeting, but she refuses to say anything without talking to someone first, who turns out to be Jenny. But before she can get back to Morse, she's found dead, tossed over the balcony. DeBryn confirms she died over the weekend. Dr. Jeremy is in, and tells Morse there are ESP researchers, and Benford was in charge of the sensory deprivation department. He and Ferman also have vague alibis for Saturday.
Morse and Thursday track down Blish at home. He lies about Molly Andrews and pretends he disapproved of Benford's nascent TV career because he thought it would distract her from serious work. (He also doesn't tell anyone he gets appointed to present the series now she's dead.) Morse notes his horrid attitude towards women, including his wife. Benford's flat has articles on Andrews, and there's a datebook with Jenny's name and "regarding MA." When they meet her, Jenny tells them she knows who killed Molly. Not that she was there, she saw it in her mind's eye. But she knows about the torn-off necklace, something Morse hadn't told anyone, since he wasn't supposed to have those photos out of the office.
Strange uncovers that everyone in the department auditioned for the TV series, a line of questioning that gets a bitter sexist rant out of Ferman, and Jeremy had a crush on Benford. Meanwhile, the boater of The Rosie Jugg dies of alcohol poisoning, and Morse and Strange are called since he had Andrews' purse. It's got Jeremy's card and phone number in it. Jeremy admits he was dating Andrews, who was a test subject, a "control" with no aptitude, mostly kept on because she was so sincere and useless. Jeremy also says she was terrified of Carl, and he believes that's who killed her.
The next night, another woman gets flashed right after hearing someone whistling, and Jenny calls, declaring she's had another vision. While Strange takes a statement hoping to turn up the flasher, Morse takes Jenny out to the towpath, where she tells him she sees Violetta when she looks at him, unsettling Morse further. Thursday goes to confront Blish and Ferman that they knew about Jenny Tate's visions. They tell him they thought Jenny was a fraud, but Thursday intimates she knew things, both in the Andrews and Benford case, that suggests her gift is real.
As Strange looks through the lists of patients, Morse notes that Blish signed off using a fountain pen, the same one found under Benford's body. Meanwhile, Blish has called Jenny in, believing she knows he killed Benford. Thursday and Morse arrive just in time to stop him from strangling her. He admits he killed Benford. Blish was obsessed with her, and misread every body language to assume she returned those feelings. When she turned him down flat, he went nuts, especially once she got the TV job over him. But of course, he blames her for leading him on, his failed rape attempt, and pushing her over the railing. Despite all this, he insists he had nothing to do with Molly's death, but Thursday and Morse are convinced they have their man.
As Morse heads to Ludo's for a party, Bright and Thursday sit and have a drink. Bright's wife is still slowly dying of cancer, turning to faith healing in her final months. Bright is desperate to understand, and Thursday reminds him faith can move mountains. Poor Thursday needed to retire years ago now (the birds are merely a symptom of his deep depression), but he's still Bright's second for life. Meanwhile, Morse runs into Violetta at the party and learns she's Ludo's wife.
Out on the towpath, Jakobssen is back, readying to expose himself to another victim. But this one was ready with a sword.