In your sentence, which is used because it introduces a non-defining relative clause. Such clauses provide additional information about a noun, but they can be removed from the sentence without changing the essential meaning of the main clause.
In the sentence you provide, Ms. Lam is stepping down as CFO next Monty is the main clause, and which means the company must seek a replacement immediately is an additional piece of information about that fact. As non-defining clauses are usually set off by commas, which is the correct relative pronoun to use here, even though there is no comma in the sentence.
If you had used that instead of which, it would imply a defining relative clause, which would change the meaning of the sentence, suggesting that there's only one CFO stepping down next month, and that specific CFO requires an immediate replacement.