に応（おう）じて is a combination of に, and the て-form of the る-Verb 応（おう）じる ‘to apply to’. This grammar structure is often translated as ‘depending on (A), (B)’, or ‘in response to (A), (B)’. However; in almost all cases, it is just indicating that (B) is something that is done in a way that is ‘applicable’ to what is necessary of (A).
に応（おう）じて will appear after nouns, or as
に応（おう）じた when directly modifying a second noun.
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日本語（にほんご）を教（おし）える際（さい）には、生徒（せいと）達（たち）のレベルに応（おう）じてクラスを分（わ）ける必要（ひつよう）があります。
When teaching Japanese, it is necessary to divide classes according to the level of the students.
この地域（ちいき）の土地（とち）は、面積（めんせき）に応（おう）じて値段（ねだん）が高（たか）くなります。
Land in this area is priced according to its surface area.
私（わたし）たちはクライアントの要望（ようぼう）に応（おう）じたデザインを提供（ていきょう）しています。
We provide designs that meet our clients' requests.
Fun-fact - 応（おう）じる usually indicates the way something ‘responds to’ or ‘answers’ an issue on a case-by-case basis. Due to this, what happens in (B) will frequently indicate something that changes depending on the intensity or severity of (A).