If she stipulated that he should not take another wife, does he have to adhere to that?

Praise be to Allah.

Firstly: 

If the wife stipulates that her husband should not take another wife, this is a valid condition and he must adhere to it; if he does take another wife, she has the right to annul the marriage contract. 

That is because of the report narrated by al-Bukhaari (2721) and Muslim (1418), that the Messenger of Allah (blessings and peace of Allah be upon him) said: “The conditions that are most deserving to be fulfilled are those by means of which intimacy becomes permissible for you.” 

And because he (blessings and peace of Allah be upon him) said: “The Muslims are bound by their conditions, except a condition that makes something permissible forbidden or makes something forbidden permissible.”

Narrated by al-Tirmidhi (1352) and Abu Dawood (3594). It was classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.

This condition does not make something permissible forbidden; rather it restricts the man’s power and gives the wife the right to annul the marriage. Such conditions were made at the time of the Sahaabah (may Allah be pleased with them). 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) was asked about a man who married a woman, and she stipulated that he should not take another wife or make her move from her home, and that she could live with her mother, and he went ahead (with the marriage) on that basis. Is he obliged to adhere to that, and if he goes against these conditions, does the wife have the right to annul the marriage or not? 

He replied: Yes, these conditions and similar ones are valid according to the madhhab of Imam Ahmad and others among the Sahaabah and Taabi‘een, such as ‘Umar ibn al-Khattaab, ‘Amr ibn al-‘Aas, Shurayh al-Qaadi, al-Awzaa‘i and Ishaaq. The view of Maalik is that if she stipulates that if he takes another wife or takes a concubine, she has the right to decide [whether to stay married to him or not], then this condition is also valid, and the woman has the right to leave him. This is similar to the view of Ahmad. That is because of the report narrated by [al-Bukhaari and Muslim] in al-Saheehayn, that the Prophet (blessings and peace of Allah be upon him) said: “The conditions that are most deserving to be fulfilled are those by means of which intimacy becomes permissible for you.” And ‘Umar ibn al-Khattaab said: “Rights are connected to conditions.” So the Prophet (blessings and peace of Allah be upon him) made that by which of means intimacy becomes permissible more deserving of being fulfilled than anything else.

End quote from al-Fataawa al-Kubra, 3/90. 

Secondly: 

These conditions only apply if they are agreed upon at the time of the marriage contract. If they occur after the marriage contract has been done, they are a promise and do not give the wife the right to annul the marriage, but the husband has to fulfil his promise, because of the general meaning of the evidence that enjoins fulfilling promises, such as the verse in which Allah says (interpretation of the meaning): “And fulfil (every) covenant. Verily, the covenant will be questioned about” [al-Isra’ 17:34] and the words of the Prophet (blessings and peace of Allah be upon him), “Guarantee me six things and I will guarantee Paradise to you: be truthful when you speak, fulfil it when you make a promise, render back if you are entrusted with something, guard your chastity, lower your gaze and restrain your hands (i.e., do not harm others).” Narrated by Ahmad (2225); classed as hasan by al-Albaani in Saheeh al-Jaami‘ (no. 1018), and because breaking promises is one of the attributes of the hypocrites. 

See also the answer to question no. 30861. 

And Allaah knows best.