[verb (dictionary form)] + につれて / につれ [noun] + につれて / につれ
につれて means "as": as one thing changes, a second thing changes with it, step by step. It goes after the dictionary form of a verb, or after a noun for a change such as せいちょう成長 or ぞうか増加.
The first half has to be a change that moves forward, and the second half a change that follows it. The end of the sentence is usually なる, きごう〜てくる, きごう〜ていく or a verb like ふえる増える. A season, a single event or a fixed fact does not fit.
The second half also can't be something you decide to do, ask for or suggest.
In the "as" meaning, にしたがって is the same and the two can be swapped. Only にしたがって also means "following a rule or instruction".
につれ is the written form of につれて.