Tamara Tunie is limbering up to play the vice-president of America in Mike Bartlett’s new political satire, The 47th. “I have great admiration for what she’s achieved,” says Tunie, in a back office at the Old Vic in London, emanating a big, easygoing exuberance that seems Californian in spirit, although she is a New Yorker. So how is she preparing for the role of Kamala Harris: observing her public persona to mimic her convincingly?

“No, I don’t try to impersonate – I find that could get in the way,” says Tunie, who appears utterly at ease with the part. Perhaps that’s because she is no stranger to playing true-life characters – including Whitney Houston’s mother, Cissy, in the upcoming biopic I Wanna Dance With Somebody. “I go to good old YouTube to see what interviews I can find,” she says of her research. “But what I look for more is the essence of the person: there might be one or two things that are significantly them – a quirk, something that they do. What I try to do is land on that but then allow myself the freedom to go: ‘What if they were in this situation?’”

Bartlett’s drama finds Harris in 2024 in a world still dominated by the Trump family. It is a funny, horrifying political dystopia, much of it written in iambic pentameter with sly Shakespearean references tucked in. The reality of living through the Trump administration was sobering for Tunie. “This undercurrent of racism and misogyny was always there. What Trump allowed was the Pandora’s Box to be flung open … We must remain vigilant, and we must constantly fight, and we can never just relax and think ‘OK, everything is taken care of.’”

Does she think America began relaxing during the Obama years? “Absolutely. The point when President Obama was elected was when the term ‘post-racial’ was coined. That was, unfortunately, a fantasy that everything was all fixed, because now we had a black president. What we are seeing – and one of the reasons I believe that Trump was elected – was that there was a backlash. In my circle we called it ‘black-lash’.”

Tunie was born and raised in Pittsburgh, one of six siblings whose parents ran a funeral home. Her mother was also the first black female security guard at United States Steel and had a strong activist streak: “She believed that if there was something that needs to be addressed, you don’t wait for somebody else to do it.” Her father had a second job as an airport porter. Tunie was an all-rounder at school who loved singing and dancing but was fiercely academic, with ambitions to become a medic (she has played a medical examiner for more than 20 years in the TV drama Law & Order: Special Victims Unit).

What made her swerve into the performing arts was a single, thrilling moment, in the choir of a spring concert at high school. “I had a solo number and I got a standing ovation. It occurred to me that ‘This makes people really happy, it is something I love to do, and I can touch people with it.’”

She won admission to the prestigious drama school at Carnegie Mellon University and made her Broadway debut in 1981. Feeling potentially pigeonholed as a musical performer, she stopped singing and dancing for a while. “I was classically trained. I wanted to do Shakespeare, I wanted to do straight plays, film and television. So for a good eight years or so I didn’t sing at all.”

What was it like to return to singing for her part as Cissy Houston, one among a family of women with phenomenal voices, filmed last year? “Utterly intimidating. A lot of people don’t know that I sing, but the music that inspires me is in the jazz vein. Cissy Houston is more an amazing singer of gospel and R&B.” Tunie re-trained her vocals to “find” the character with the help of a musical team which included Rickey Minor, Whitney’s musical director.

The 47th is the first live show Tunie has done since the beginning of the pandemic but she used the shutdown to build a campaign for better inclusivity within the theatre community. As part of Black Theatre United, the organisation which Tunie co-founded with fellow black professionals, a “New Deal for Broadway” was secured last year, which established industry-wide standards for equality, diversity, inclusion and accessibility. “This was a product of six months of meetings with the leaders in the industry: theatre owners, producers, creatives, casting directors. It is not a legal document but an agreement that is saying we as a community are going to address the exclusions of black people and make the industry much more inclusive.”

Has she seen change more generally across screen and stage in recent years? Yes, but it has come very slowly and with a lot of pain. And even then it could flip back, she says, returning to her point about remaining vigilant. “But what I see in Hollywood are black individuals who have their own production companies, and black people making their own content, with Hollywood calling on them. There is Shonda Rhimes and the incredible dynasty she has built … I see that here, too [in the UK] – I worked with Michaela Coel in Black Earth Rising and she is very much the example of what I’m talking about.”

On the subject of trailblazing women, has she ever met Harris? “I was on a Zoom with some other black women [during the presidential campaign] and she chatted with us, sharing some of her thoughts and policies for the future of the country. I found her utterly engaging.” So Harris for president? “As Jesse Jackson would say, ‘I keep hope alive.’ [To be vice-president] is a monumental accomplishment and I feel like it’s another rung in the ladder towards equality and space for not just a woman but a woman of colour to be the president of the United States. That would be the best thing for the country.”

• The 47th is at the Old Vic, London, from 29 March to 28 May.