Like
それに,
それで is another 接続詞（せつぞくし） (conjunction) that is regularly considered to be one word in Japanese, but is more correctly just a combination of the 代名詞（だいめいし） (substitute noun)
それ, and the 格助詞（かくじょし） (case-marking particle)
で.
The thing that
それ is ‘substituting’ for is the entire clause/sentence that came before it, while
で highlights that ‘with that’, or ‘by means of that’. In this way, it translates to ‘therefore’, ‘because of that’, or ‘with that’ where ‘that’ is the previous information.
それで is frequently used at the beginning of a second sentence, to highlight the information from the first.
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私（わたし）は子供（こども）のころにお医者（いしゃ）さんに命（いのち）を救（すく）われた。それで医者（いしゃ）になろうと思（おも）った。
A doctor saved my life when I was a child. Due to that, I became determined to be a doctor.
-
彼（かれ）は電車（でんしゃ）の中（なか）で痴漢（ちかん）をした。それで彼（かれ）は警察（けいさつ）に捕（つか）まった。
He groped someone on the train. As a result of that, he got arrested by the cops.
You may also see
それでは.
で in this case is the 連用形（れんようけい） (conjunction form) of
だ (the auxiliary verb). Due to this, the meaning is closer to ‘well then’, ‘in that case’, or ‘if so’. This
では is also frequently shortened to
じゃ.
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サリーは世界中（せかいじゅう）のほとんどの国（くに）に行（い）ったことがある。それで旅行会社（りょこうがいしゃ）で働（はたら）くことにした。
Sally has been to most countries in the world. Because of that, she decided to work at a travel agency.
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それでは、会議（かいぎ）を始（はじ）めます。
Well then, I will start the meeting.
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それじゃミクは来（こ）ないの？
In that case, Miku, are you not coming?