When Zlata was still a young child the family moved to Chișinău, where she went to the Romanian primary school for girls and studied violin from her father.
During World War II, Zlata was evacuated with her mother to Central Asia, but was separated from her in transit and ended up in the city of Namangan in Uzbekistan, where there was typhus and typhoid fever.
She studied composition with Leonid Simonovich Gurov (1910–1993), and violin with Iosif Lvovich Daylis (1893–1984).
She was the Honored Artist of the Moldavian SSR (1974), winner of State Prize of Moldova (1982), and Chevalier of the Order of Work Merit.
[4][5] Tkach composed about 800 works, including sonatas, string quartets, suites, vocal music, choral and instrumental works, cantatas, opera, ballet, instrumental miniatures, children's songs, and music for drama, cinema and theater.