It's important to communicate even the things you don't think you need to say at work.
You shouldn't assume other people get everything at work, rather it's important to tell others everything you need to.g you need to at work.
この場合、次のような言い方ができますよ。
ーIt's important to communicate even the things you don't think you need to say at work.
「職場で、言う必要がないと思うことでも伝えることが大切です」
things you don't think you need to say「言う必要はないと思うこと」を使って表現できます。
ーYou shouldn't assume other people get everything at work, rather it's important to tell others everything you need to.
「職場の人が全て理解できると思い込むべきでない。むしろ必要なこと全てを伝えることが大切だ」
to assume で「思い込む・当然だと思う」を使って to assume other people get everything at work「職場の人たちが全部理解して当然だと思う」のようにも表現できます。
ご参考まで！
カナダ 
