Earlier this year she sent audition videos to several European schools, including the Royal Conservatoire in Scotland which she also got in to, but Rambert was her top pick.
"The more I learnt about it the more I was interested because they have a kind of equal amount of ballet and contemporary training which I'm really into and you do lots of choreography as well and I love that."
Smith was equally excited when she found out Zoe had been accepted into Rambert.
"I couldn't believe it and I had to give her a double hug.
"It's a hugely prestigious school . . . so we're extremely proud that one of our students has been accepted."
It was rare for New Zealanders to be accepted into the school. Smith said she knew of only one or two other Kiwis who'd attended and Zoe had worked hard get in.
"She's on her next step now to achieving her dream, so it's wonderful."
In September Zoe will start a three year course in ballet and contemporary dance at Rambert, which counts former Royal New Zealand Ballet dancer Cameron McMillan - who now works as a freelance dancer and choreographer in London - among its alumni.
After completing her degree she hopes to get in to the Royal New Zealand Ballet or Netherlands Dance Theatre as a professional dancer.
"Then I'd like to choreograph my own works - that'd be really rewarding I think," Zoe said.
Course fees for the year 2017-18 are £17,850 for overseas students, the school's website says.
She's not the only Kiwi dancer with big dreams who is making her mark on the ballet world.
Another of Smith's students, 16-year-old Isabel "Izzie" Bloomfield, will attend the summer school programme at the Academie de Princess Grace in Monaco, Monte Carlo in July.
"I'm staying at the boarding school, which is really exciting because I'll get to see all the facilities, and it's really intense - it's five and a half days, from 9 till 6, of just ballet," Izzie said.
"Hopefully from that summer school I'll be getting into their full time programme."
