Since her parents were Jewish, the most "obvious" explanation is surely that they used this as an alternative for
Sara or
Sarah.
In her book "The History of
Christian Names" (google it), page 48, the 19th century British pioneer of name meanings and usage
Charlotte Mary Yonge gives
Zara as an "eastern" form of
Sarah, meaning "princess".
Here in Australia, there was a well-known public figure called
Zara (Dame
Zara Bate, whose second husband,Harold Holt, was prime minister of this country in the 1960s. She was born in 1909, so it may be that the name was mildly fashionable in English-speaking countries at that time.
If you enter the name into the Google Books search option you may turn up something literary, dating to that period.
There is, for instance, a long work, "
Zara ... a poem of the sea", dating to 1833, published in
London, so the name was certainly known by the time your ancestor was born.