Tennet made her first television appearance on an anti-smacking commercial at age 7. Soon afterwards, she appeared on Xena: Warrior Princess as a little runaway princess named Alesia in one episode of the series' fourth season (1999). She later appeared in the movie Kids World as Nicole Mitchell, a role for which she won the Best Juvenile Performer Award at the 2000 Nokia New Zealand Film Awards for her role in the movie.
Following this, Tennet had had a leading role in the short film Watermark. The film received many awards, including a personal one for Best Actress, at the 2003 New Zealand Drifting Clouds Film Festival in Wellington. She would then gain her biggest international exposure yet playing a small speaking part in Peter Jackson's adaptation of J. R. R. Tolkien's The Lord of the Rings: The Two Towers, as a young Rohan girl named Freda. She can be seen fleeing a burning village on a horse along with her onscreen brother Éothain.
A few years later, Tennet would play the role of the circus performer Lilith in the post-apocalyptic children's fantasy Maddigan's Quest (2006). A year later, she would gain her biggest television role yet on Shortland Street as Tuesday Warner for the 2007 and 2008 seasons.
Following her time on Shortland Street, Tennet played the role of the scientist Dr. K on the American children's television show Power Rangers RPM (2009). Her most recent on-screen appearance was on the New Zealand comedy The Almighty Johnsons as Delphine (2011).
Tennet is also an experienced stage actress in New Zealand, having participated in both amateur and professional theatrical performances in shows like 360˚ and Stepping Out. In June 2009, she and a classmate from her secondary school traveled to London to participate in three weeks of acting workshops conducted at the Globe Theatre with the Young Shakespeare Company, being taught by tutors from both the Globe Theatre and the Royal Shakespeare Company. She will soon appear in two productions with the Peach Theatre Company: the first as Emilia in Othello in late July, and the second as Dorothy in The Wizard of Oz in September.
Aside from her acting talents, Tennet is also an accomplished dancer. She has competed and won awards in several dancing competitions in New Zealand. She also has a YouTube channel featuring her performing jazz, tap, and hip hop dance choreography. She also worked on choreography for Sirens, a water ballet show put on by the Wet Hot Beauties for the 2011 Auckland Fringe Festival.