She was born in Argos Orestiko in Greece but moved to London when she was twenty. Her first full-length play, Ithaka, started as a short story written as a result of participating in a writers' workshop. It was turned into a performance and then she was asked to extend it into a full-length play for a rehearsed reading at the Riverside Studios, Hammersmith, in June 1989.
Rapi studied Sociology at the London School of Economics. She then took an MA course in drama at the University of Essex. While there she wrote the one-woman show Johnny is Dead, which was later produced as part of the first one-person play festival at the ETC Theatre in London in 1991.
She then received a commission by Aspect Theatre Company to write a full-length play for the Oval House, and Dream House, was the result. The author was bemused when heterosexual actors insisted that they knew more about the sexuality of their characters than the writer - especially when that sexuality was assumed to be heterosexual when the author had clearly written it as lesbian.
Rapi was then commissioned by Broadsword Theatre Company, a Greek-Cypriot British company, to write a play about the Greek Civil War for female actors, and Dance of Guns was the result. Heterosexual actors considered playing the two central characters who were lesbians as "... the most difficult acting experience so far", and insisted that no lesbians were involved in the Greek Civil War, and even more that no lesbians actually existed during the forties - despite evidence to the contrary. Considerable, and in the author's view, unnecessary argument took place around these issues, detracting from precious rehearsal time. The play toured London in the Spring of 1992 and played at various venues, including a Turkish community centre in London where it received a standing ovation.
Another commission followed which resulted in the monologue Dangerous Oasis, produced at Finborough Theatre, part of the award-winning Women's Work Season, 1993. She was editor of the lesbian and gay theatre journal Glint, from 1993 to 1995.
Nina Rapi felt this series of commissions as inhibitive to her artistic freedom. As a result she took a break to clarify her ideas. Out of that emerged Edgewise in 1996 which has so far received brilliant theatre reports but no production. It did however have a reading at Eros Theatrou, Athens, Greece in October 2000. It also led to a theatre writing bursary from the Arts Council in 1998 which produced Angelstate, an extract of which Confession was a prize-winner at the London Writers Competition in 1999.
During 1999, she also wrote Lovers and Other Enemies which was a finalist, hotly debated to be a winner, at the Future Perfect Competition 2000. It had a rehearsed reading at Three Mills Studio in June 2000.
Rapi is a part-time tutor in Creative Writing at Birkbeck College, and was visiting lecturer at Goldsmiths College, University of London from 1995 to 1998. She was a researcher/writer for the Channel 4 television documentary Greek Love and Sapphic Sophistication, (1990).
In 2001 Nina Rapi developed No Trouble with a bursary and dramaturgy from Soho Theatre. Another 2001 production is Lovers at the Gielgud Theatre, West End Shorts, London New Play Festival. She teaches Creative Writing part-time at Birkbeck College, London.