Grammer was born in Los Angeles, California to actor Kelsey Grammer and make-up Artist Barrie Buckner. Her parents were never married. Through her father, she has three half-sisters: Spencer (born 1983), Mason (born 2001), and Faith (born 2012) and three half-brothers: Jude (born 2004), Gabriel (born 2014), and James (born 2016). She was raised primarily by her mother in Malibu, California. She was named after Actress Greer Garson.
Grammer entered her first beauty pageant in 2008, winning the title of Miss Teen Malibu. She went on to place within the top 10 in the Miss California Teen competition. She competed again the following year, successfully retaining her crown and again placing within the Top 10 of the state competition. In 2009, she represented the Marina Del Rey region, placing in the Top 10 of the 2010 state competition for the third year in a row. That year, Grammer also held the title of Miss Regional California Teen 2011.
Grammer's first acting role was as a guest star on an episode of the Nickelodeon teen series iCarly in 2010. She then went on to star in the independent films Almost Kings, Chastity Bites, and An Evergreen Christmas.
In 2011, Grammer was cast as Lissa Miller in the MTV comedy series, Awkward. She was in a recurring role for the first two seasons before being promoted to a series regular for seasons three, four and five. In 2015, she guest starred as McKenna on Melissa & Joey for three episodes of the final season.
Grammer became passionate for theater at a young age, participating in various plays from the age of 5 before competing in pageants as a teenager. She attended Idyllwild Arts Academy for two years, receiving training under their theater program. She graduated from the University of Southern California in June 2014 as a theater major. She is also a member of the Delta Tau chapter of the Kappa Kappa Gamma sorority.
It was announced in June 2015 that Grammer would be starring in the upcoming Lifetime original movie, Manson's Lost Girls, to be released in 2016. In July 2015, it was announced that she would be starring as Summer Roberts in The Unauthorized O.C. Musical, a stage adaptation of the pilot episode of The O.C..
In 2016, Grammer began a recurring role on the ABC sitcom The Middle, playing Axl Heck's girlfriend April.
