I won't allow my daughter to have a smart phone until she is 15 years old (becomes a high school student).
I won't let my daughter have a smart phone until she turns 15.
I won't let my daughter have a smart phone until she enters high school.
I won't let my daughter have a smart phone until she is 15 years old.
let+誰か+動詞の原形 ですので、to はいらないです。
もしくは allow =「許す」を使うなら以下のようにもできます。
I won't allow my daughter to have a smart phone until she becomes a high school student.
high school student には a がつきます。
より自然な言い方をいくつか挙げるなら、
I won't let my daughter have a smart phone until she turns 15.
娘が15歳になるまで携帯を持たせないだろう。
15歳に「変わる」のturnを使う方が、なった瞬間からOKという感じが出ます。years old も文脈で分かるなら省略されることが多いです。
I won't let my daughter have a smart phone until she enters high school.
娘が高校に入るまで携帯を持たせないだろう。
goes to high school でもいいと思います。