The three-minute teaser shows the pair, played by Gillian Anderson and Olivia Colman respectively, during a tense skirmish early in the former Conservative leader’s premiership.
During one of their first official meetings, Baroness Thatcher says: “I think we have enough respect for one another personally to ask ourselves some of the bigger questions, woman to woman. We are the same age after all. Just six months between us.”
The Queen asks: “And who is the senior?”, before Baroness Thatcher replies coldly: “I am, ma’am.”
Viewers glimpse the prime minister sitting in Parliament before the trailer cuts to footage of the Falklands War and the miners’ strikes.
The Duke of Edinburgh, played by Tobias Menzies, is heard saying: “Two women running the shop. That’s the last thing this country needs.”
But the Queen replies: “Perhaps that is precisely what this country needs.”
The Prince of Wales’s romance with a young Princess Diana also comes under the spotlight, played by Josh O’Connor and newcomer Emma Corrin.
The fourth season begins in the late 1970s as the Queen and her family attempt to safeguard the line of succession by securing an appropriate bride for Charles, who is unmarried at 30.
Britain’s first female prime minister, Baroness Thatcher, creates conflict with the Commonwealth after leading the country into the Falklands War, only increasing friction with the palace.
Writer Peter Morgan said: “It could be said that they are two very similar women, born only months apart.
“They are very much defined by the Second World War, by a sense of frugality, hard work, commitment, Christianity and so much more.
“It was a commonly held piece of wisdom that the Queen and Thatcher didn’t get on. I think there was probably a lot of respect.
“But they also had many differences, it was really fun exploring their differences and their similarities. I also get a chance to explore them both as mothers.
“Writing Thatcher and the Queen as mothers was probably an angle that no-one has explored before. But it yielded one of my favourite episodes in the season.”
Speaking about his portrayal of Diana, he said: “Diana now has a historical perspective. I am really conscious of that. I really don’t want to get too close so that what I do is journalistic.
“I really want to make sure that there is enough distance so that if you tell the story of Diana it can almost be something else. It can have metaphorical resonance.”
The fourth series also stars Helena Bonham Carter as Princess Margaret, Erin Doherty as Princess Anne and Marion Bailey as the Queen Mother.
Season four launches on Netflix on November 15.