Abi Morgan, the writer behind films such as The Iron Lady and Shame, as well as television dramas including The Hour, is to make her debut at the Royal Court theatre with a play based on 40 years of transcripts charting a real-life extramarital affair.

The Mistress Contract is, according to Vicky Featherstone, who will direct the play, about "decay – whether we can stave off decay".

The American couple in question, whose identities have not been made public, knew each other at university, fell out of touch and met again 20 years later. Having begun an affair in 1981, some time later the woman sent her lover a fax containing a contract. She would provide sex and "mistress services"; he would provide a house in which she could live in comfort and she would record all their conversations and intimacies. He accepted her terms by return.

The play is also a "cultural journey through their love of art, literature and books", said Featherstone, charting decades of intellectual to-and-fro between the pair, whose contract continues into their old age. Recording their conversations was, said Featherstone, also about "trying to keep hold of something; persuading yourself that something is not transient".

Featherstone, unveiling her first season for the Court, where she has been artistic director since April, also announced that Dennis Kelly, writer of the recent Channel 4 drama Utopia and Matilda, the Royal Shakespeare Company's musical adaptation of the Roald Dahl story, is to make his debut at Britain's most important theatre for new writing.

The Ritual Slaughter of Gorge Mastromas is a dark morality tale about "capitalism, greed and individualism", said Featherstone, who will direct. The central character is a man born in the 1970s who "is offered a chance to be really successful", she said. "The play asks, if we pursue that, what happens when all those promises collapse?"

In the new season, which begins in September, the theatre will also address different aspects of Muslim life via a trio of new plays. Routes, by Birmingham playwright Rachel De-lahay, is about six men aged 15 to 28, each with a different experience of immigration to Britain; Featherstone described it as "very witty, funny, clever and with extraordinary dynamism". The Djinns of Eidgah, by the Bangalore-based Abhishek Majumdar, examines the experience of young Sufi Muslims in Kashmir; while the third work is Suhayla El-Bushra's new play Pigeons, directed by Carrie Cracknell. About two British teenagers, Amir and Ashley, whose friendship is tested by the creep of prejudice, Pigeons will tour London schools in the autumn term this year.

The third debutant playwright on the Royal Court's main stage is Jack Thorne – one of only three male writers in the main programme (leaving aside Samuel Beckett, three of whose short works will be performed by actor Lisa Dwan).

Thorne, whose TV writing includes the Bafta-winning This Is England 88, will bring to London his adaptation of the vampire film and novel Let the Right One In, after an acclaimed run with the National Theatre of Scotland and before it transfers to the West End. The pitch-black, oddly touching story is directed by John Tiffany, the new associate director of the Court, which staged Black Watch.

The Royal Court's Christmas show will be conceived by a group of writers including April de Angelis and Nessah Muthy – the latter an usher at the theatre as well as a playwright. Described as "an edible performance", the show is titled Gastronauts and will be, quite literally, a feast, with food and conversation.

Featherstone said that she had been "brilliantly surprised" that the arts had received a relatively light 5% cut at the comprehensive spending review last month, and was fortunate that she was inheriting a theatre that was "seen as a vital part of Britain, and England's theatre scene". Future plans include, she said, working more with theatres outside London to fulfil the Court's national remit – for example co-producing plays and setting up a touring circuit.