She won the Tudor Award for Best Actress at the International Filmfestival Geneva for her role in "Deep" (Diep, 2005). She won a nomination for Best Actress at the Dutch FilmFestival for here role in "Deep" (Dutch equivalent of the Academy awards) She won a Rembrandt Award (People's Choice award) for Best Actress, for her role in Winter in Wartime" (Oorlogswinter, 2008). She won the Kemna Award for best and most outstanding actor at the International Theatreschool Festival in Amsterdam 2014.

In June 2007, Klaver's boyfriend, Timo Smeehuijzen, was killed by a suicide attack during his military Service in Afghanistan.

Klaver was born in Amsterdam, Holland and grew up in the suburb town Abcoude. She has two older sisters, presenter/actress Kimberley Klaver and Dancer Stephanie Klaver. She finished her VWO (pre-university secondary education) on her high school 'Sint Nicolaas Lyceum' in 2008. She received her professional training (BFA in Acting) at the Maastricht Academy of Dramatic Arts, where she graduated in July 2014.. She also went to the Lucia Marthas Dansacademy from her 4th till the age of 15, from which she had to quit due to her busy acting schedule.

When she was 15 years old she got nominated for a Golden Calf for Best Actress (Deep), which made her the youngest Actress ever to be nominated for this award. She lost it to Carice Van Houten (Blackbook). Later she did win the Tudor Award for Best Actress (Deep) in Geneva and a Rembrandt Award for Best Actress (Winter in wartime). In 2010 she got accepted by the Maastricht theatre academy and graduated 4 years later (BFA in acting). At the International Theatre school Festival 2014 in Amsterdam she won the Kemna Award for her role as Irina Arkadina in ‘The Seagull’ (Checkov) for best and most outstanding graduating actor/actress of the Netherlands and Belgium. Before and after her education Melody played (lead) roles in art-house films such as ‘Northern Light’ (Langer Licht) by David Lammers, ‘Deep’ (Diep) by Simone van Dusseldorp, ‘Dusk’ (Schemer) by Hanro Smitsman and in box-office hits such as ‘XTC just don’t do it!’ (Afblijven!) by Maria Peters and ‘Winter in Wartime’ (Oorlogswinter) by award-winner Martin Koolhoven. On television Melody was seen in the One-night-stand series film (50 min. films) ‘Once upon a Ladder’ by Eva Zanen, ‘Near Neighbours’ by Marleen Jonkman and in series like ‘Godforsaken’ (NPO) ‘Intoxicated’ (NPO) and ‘The Jackpot’ (SBS6). Melody is currently shooting the English-spoken shortfilm ‘The Whisk’ by Sanne Kortooms, in which she plays the Hungarian Daniëlla Fehér.