She has also portrayed Lily Montgomery in All My Children and Clarisse La Rue in The Sea of Monsters film adaptation, and has made appearances on Grey's Anatomy, Terminator: The Sarah Connor Chronicles, Scoundrels, Wizards of Waverly Place, and CSI: Miami.
Rambin was born in Houston, Texas. Her father, Joseph Howard Rambin III, is co-founder of Moody-Rambin, the largest locally owned commercial real estate firm in Houston. Her mother is the former Karen Stacy Guthrie. Her older brother, Joseph Rambin, is currently enrolled at The University of Alabama. Her older half-sister is Mary Rambin, blogger of "More Than Mary" and designer of the Moe handbag line, currently residing in Houston, Texas. She is the granddaughter of J. Howard Rambin, Jr, former CEO and president of Texaco oil company. She began performing in school plays. She studied at the Houston School of Film and Theatre and at St. Francis Episcopal Day School where she starred in her first school play before relocating to Connecticut and later New York when she was cast on All My Children (her first professional acting role). While acting, she has also pursued her high school diploma through the Texas Tech University Independent School District.
Rambin joined the cast of ABC's All My Children in February 2004, portraying the role of Lily Montgomery, the autistic daughter of Jackson Montgomery.
On March 30, 2007, Rambin had dual roles on All My Children, playing the autistic Lily Montgomery, as well as her street-smart but lovable older half sister, Ava Benton. She later appeared on an episode of Law & Order: SVU. On February 28, 2008, Leven appeared on NBC's series Lipstick Jungle. Leven will appear in film for the first time in Killer Film's independent picture, Gigantic. The film stars and is produced by Paul Dano. Leven filmed a pilot presentation for the CW titled "Austin Golden Hour", directed by Sanford Bookstaver in April 2008. Leven also appeared in the ETC series "One Three Hill."
Rambin was the only actress from All My Children to be nominated for the 34th Annual Daytime Emmy Awards. She was nominated for "Outstanding Younger Actress in a Drama Series" for her roles as Lily Montgomery and Ava Benton.
In September 2008, Rambin joined the cast of Terminator: The Sarah Connor Chronicles as a series regular, playing the character Riley Dawson, a school friend and love interest of John Connor. Rambin left the show after filming her last episode, "Ourselves Alone".
She has been signed to Wilhelmina Models.
In 2009, Rambin landed a recurring role as Sloan Riley, the 18-year old-daughter of Dr. Mark Sloan on Grey's Anatomy.
Rambin briefly returned to All My Children as Lily Montgomery on January 5, 2010 for the show's 40th Anniversary.
In March 2010, Leven was cast as the daughter of Virginia Madsen and David James Elliott on the ABC series Scoundrels.
Rambin posed as Elizabeth and Jessica Wakefield for the new version of Francine Pascal's popular book series Sweet Valley High.
In February 2011, Rambin appeared on the Disney Channel show Wizards of Waverly Place in the recurring role of "Rosie"(Wizards vs.Angles special event). In February 2011, she was cast in the recurring role of "Chloe Hall" on the long-running CW series One Tree Hill. She will first appear in the role on the 16th episode of the 8th season. In February 2011, Leven was cast as Molly Sloan on the CBS crime drama CSI: Miami. She first appears in season 9 episode 14 where she quickly makes a solid first impression on CSI Ryan Wolfe.
In April 2011, it was announced that Lionsgate and director Gary Ross cast Rambin in her first major studio film, in the role of Glimmer in the film adaptation of the The Hunger Games.
She was supposed to return to AMC in August 2011 before the show's ABC network end in September, but her appearance had to be canceled due to a time conflict with her production schedule for The Hunger Games.
In September 2011, Rambin was cast as the female lead in the surf biopic Of Men and Mavericks, about the life of surfer Jay Moriarity.
In late April 2012, Rambin was cast in a lead role in the Percy Jackson: Sea of Monsters. She portrayed Clarisse La Rue, a daughter of Ares.
Rambin got engaged to producer Geoffrey James Clark in 2009 in the Bahamas. They broke off their engagement in November 2011.