"Shylock is one of the most commonly reviled characters in Shakespeare," Stewart said.
The Los Angeles based actor - best known as Captain Jean Luc Picard - was born in Mirfield in West Yorkshire.
Shakespeare's Alien is an exploration of the character of Shylock - a Jewish moneylender who appears in Shakespeare's The Merchant of Venice.
The one-man show is a personal project for Stewart who was nominated for an Olivier award for his performance in The Merchant of Venice.
"Shylock is one of the most commonly reviled characters in Shakespeare," Stewart said.
"Through perfomance and analysis I try to reveal him as a more understandable and even sympathetic character than he is normally thought to be."
After-show discussion
Shylock is portrayed as a cunning scoundrel, something that is either interpreted as Shakepeare's attempt to convey the anti-semitism of Elizabethan society or evidence of the playwright's own anti-semitism.
After each performance there will also be the unique opportunity to enjoy an open after-show discussion with Stewart.
In the Autumn he will take the lead role in the JB Priestley play Johnson Over Jordan - also being staged in Leeds.
Stewart will star as a man looking back over his life in the play, which will be directed by Jude Kelly.
Kelly, artistic director at the West Yorkshire Playhouse, previously directed Stewart in Othello at the Shakespeare Theatre in Washington DC.
Although the actor is best known for his screen role in Star Trek: The Next Generation, he has had a long and successful career in the theatre.
String of awards
He began acting in theatre groups at the age of 12 and is an honorary associate of the Royal Shakespeare Company.
Other than Star Trek, his television appearences include BBC productions of I Claudius, Smileys People, and Tinker, Tailor, Soldier, Spy.
He has won a string of awards, including the London Fringe Theatre Best Actor Award 1986 for his portrayal of George in Who's Afraid Of Virginia Woolf.
His most recent honour was an OBE in the New Year's Honours list.