Tamar Narkiss-Melzer started playing the oboe at the age of fifteen. In 1985, she graduated from Tel Aviv University, where she studied with Eliahu Torner, and won first prizes in concerto and chamber music competitions.

While staying in the United States between 1985 and 1992, she continued her studies with renowned oboists including Ray Still, John DeLancie, Sarah Lambert-Bloom, and Richard Killmer.
She has also played in the US in various ensembles and orchestras, such as the Chicago Civic Orchestra, the Sarasota Festival Orchestra, and the Miami City Ballet Orchestra, where she served as Principal Oboist during the 1990-91 season.

After returning to Israel, Tamar joined the Israel Philharmonic, where she has played since 1992. She also takes part in chamber music concerts throughout the country.