〜につれて

as (one thing changes, so does another)

Verb dictionary form / Noun + につれて

につれて links two changes: as the first progresses, the second follows. 年をとるにつれて、体が弱くなる, "as you get older, your body gets weaker".

Both parts describe gradual change, so the verbs are words like なる, 増える, 上がる, 近づく, 慣れる, 経つ. It doesn't work for a single event: not ベルが鳴るにつれて.

It's very close to にしたがって and とともに. につれて sounds a little more natural in speech, and focuses on the second change naturally following the first.

Compare ながら, which is one person doing two actions at once, not one change dragging another along.

Examples

年としをとるにつれて、体からだが弱よわくなる。
As you get older, your body gets weaker.
時間じかんがたつにつれて、悲かなしみは薄うすれていった。
As time passed, the sadness faded.
山やまを登のぼるにつれて、気温きおんが下さがってきた。
As we climbed the mountain, the temperature dropped.
日本語にほんごが上手じょうずになるにつれて、日本にほんの生活せいかつが楽たのしくなった。
As my Japanese improved, life in Japan became more fun.
試験しけんが近ちかづくにつれて、不安ふあんになってきた。
As the exam got closer, I started getting anxious.