Can a wife put the condition "the husband will not marry another" in a contract in Saudi Arabia?

Yes, and in Hanbali fiqh, the basis of Saudi law, that condition is valid and binding; if it is breached, the wife may choose fasakh. Article 27 of the Personal Status Law 2022 binds the couple to agreed conditions, but it only gives a right to fasakh if written in the contract document or acknowledged by both parties. Article 28: if the husband breaches a condition, fasakh takes place without compensation from the wife. The evidence is the hadith: "The conditions most deserving of fulfilment are those by which you make intimacy lawful" (Sahih al-Bukhari 2721; Sahih Muslim 1418). However, some Saudi scholars argue that such a condition can be voided under Article 29, and how far the courts enforce it after 2022 is to be verified. Make sure the condition is written in the registered contract. See Saudi Arabia.