In this structure the first clause ends in a -te form verb, which is then followed by a second clause. The important thing to note here is that the verbs not closely linked: The second verb can take its own arguments, and both clauses, even though linked, have their own meaning
Examples
こちら右へ曲がって、次の信号でまっすぐ行って、すぐ郵便局になります。
Turn right here, then go straight at the next traffic lights, then you’ll soon get to the post office.
昨日は勉強しないでテレビを見ていました。
I didn’t study yesterday, I was watching TV.