Assata Shakur is alive and well in Kalungi Ssebandeke's debut play. A former ringleader of the Black Liberation Army, she was added to the FBI's most wanted list in 2013, 40 years after the roadside shoot-out that led to a state trooper's death. To her detractors, she's a terrorist; to her defenders, a scapegoat. Her surname's made her a cause célèbre: she's Tupac's great aunt and godmother.

Assata Taught Me finds her holed up in Havana, where she's lived in self-imposed exile since 1984. Despite breaking jail, she's still stuck behind a triple-locked door and, with every knock, she pulls a pistol from a plant pot - a measure of what a $2 million bounty will do to a life. This is a woman for whom riches stem from "letting people in." The irony is inescapable.

Ssebandeke imagines her opening up to a young Cuban student Fanuco Maceo (‘Blackie' to his friends and to Assata's dismay) desperate to emigrate to Miami. Having persuaded her to teach him English in preparation, Fanuco finds himself schooled in racial politics, pushed to own his blackness and honour his ancestry.

It's almost a twist on Willy Russell's Educating Rita – not just language lessons laced with class warfare, but a student aspiring to everything his tutor despises. Fanuco's infatuation with all things American, from its hip-hop stars to its suave black president, runs counter to Assata's unswerving anti-capitalist, anti-imperialist stance.

Ssebandeke captures, brilliantly, the ambiguity of Assata herself. Adjoa Andoh, staunch as hell, treads a tightrope between conviction and crackpot. A woman devoted to a righteous cause, founded on good grounds, sometimes looks positively unhinged. Behind closed doors, rum-soaked, she chats to a photograph of her late grandmother, and the bitterness of exile has contaminated her view of America.

She is, Ssebandeke makes clear, stuck in the past, listening to old vinyl records and clinging to old enmities. Is that down to her - a woman who puts her African ancestry ahead of her American identity – or down to the country that cast her adrift? Cuba's a time-warp of its own, after all, and it's a fascinating point from which to ask whether America's actually changed at all in 50 years, weighing up Black Lives Matter against President Obama. It was, of course, on his watch that Assata's bounty was imposed.

Hence the play's concern with words and action – a smooth-talking president who does next to nothing – and the tendrilis of that stretch stretch from Assata's lessons to her actions. Is her activism undermined by violent means? Does the label ‘terrorist' alter her cause?

For all its eloquence and insight, however, the play can feel contrived. Ssebandeke's guilty of convenient contradictions – Fanuco's stilted essay comes with a nuanced dissection of rhetoric – and, too often, his symbolism leads his situation. A climactic act of violence goes way too far: a stark image of infighting and generational divisions, it nonetheless involves a 70-year old woman, who's lived peaceably for 30-plus years, lynching a fighting fit 21-year old man. With more patience and attention, the play might both earn its ending and add up to a comprehensive portrait of its protagonist. As it is, there are gaps.

But better a play that does too much than too little, and Lynette Linton's production is nothing if not pulse-quickening. Jack Weir's lighting and Richard Hammarton's sound up the ante considerably, but the tension comes, first and foremost, from two combustible performances. Debutant Kenneth Omole combines Fanuco's heart with his hot-headed swagger, and Andoh is absolutely captivating at all times, utterly unpredictable and entirely inscrutable. But what's Assata Shakur if not an enigma, even after all this time?

Assata Taught Me runs at the Gate Theatre until 27 May.