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

Yes, and in Hanbali fiqh, on which Saudi law is based, such a condition is valid and binding; if it is breached, the wife may choose annulment (fasakh). Article 27 of the Personal Status Law 2022 binds the spouses to the conditions they agreed, but it grants the right of annulment only if the condition is written in the marriage contract document or acknowledged by both parties. Article 28: if the husband breaches the condition, annulment takes place without compensation from the wife. The proof is the hadith: "The conditions most deserving of fulfilment are those by which you make intimacy lawful" (Sahih al-Bukhari 2721; Sahih Muslim, Kitab an-Nikah). However, some Saudi scholars argue the condition can be voided under Article 29, and how far the courts enforce it after 2022 needs check with the authorities of the country concerned. Make sure the condition is written into the registered contract. See Saudi Arabia.