につれて・にしたがって: the difference
につれてN3
Meaning
As…then, In proportion to,
Past papers
Tested 3 times in past papers
Example
日がたつに連れて、怪我が悪化してきた。
As the days go by, my injury gets worse and worse.
にしたがってN2
Meaning
As, Following, As then, According to, In accordance with
Past papers
Tested 4 times in past papers
Example
この原稿に従ってインタビューに答えてください。
Please answer the interview in accordance with this manuscript.
How to tell them apart
「につれて」: only 'as things change'; it cannot mean obeying: not 「指示につれて」.
「にしたがって」: can mean both changing along with something and following instructions or rules.
「に伴って」: leans toward side effects of a big change.