Praise be to Allah.
It is not permissible for a man to give zakaah to his wife according to the consensus of the scholars (may Allah have mercy on them), because that is the share of the poor and needy. For more details please see the answer to question no. 130171.
If the wife is divorced, then one of two scenarios must apply:
1.It is a revocable divorce, or
2.It is an irrevocable separation, as in the case of khula‘ or a third talaaq after which the ‘iddah has ended.
If it is a revocable divorce, it is not permissible to give zakaah to her, because the wife who has been divorced with a revocable divorce is still a wife and she has the same rights and duties as any wife except in exemptions mentioned by the scholars such as a share of the husband’s time [in the case of a plural marriage] and maintenance in the case of wilful defiance (nushooz). See the answer to question no. 112002.
But if it is an irrevocable divorce, as in the case of a third talaaq or khula‘, even if her ‘iddah has not yet ended, then she is a “stranger” or non-mahram to him, so if she is entitled to zakaah, it is permissible to give zakaah to her, because she is included in the verse in which Allah says (interpretation of the meaning): “As-Sadaqaat (here it means Zakaah) are only for the Fuqaraa’ (poor), and Al‑Masaakeen (the poor) …”[al-Tawbah 9:60].
And because the husband is no longer obliged to spend on her maintenance, so it is permissible for him to give zakaah to her.
That applies unless she is pregnant, because if she is pregnant then her ex-husband is obliged to spend on her. But if she is not entitled to zakaah, such as if she has relatives who are spending on her, then it is not permissible to give her zakaah because she is not included among the categories mentioned in the verse, and because the Prophet (blessings and peace of Allah be upon him) said: “One who is independent of means or who is strong and can earn a living has no share of it.” Narrated by Abu Dawood (1633) and classed as saheeh by Shaykh al-Albaani (may Allah have mercy on him) in Irwa’ al-Ghaleel (876).
In the commentary on Qalyoobi wa ‘Umayrah (3/197) it says: The one who is sponsored by a relative or a spouse is not poor, according to the more correct opinion, because he is not in need; this is like the one who can earn every day enough to suffice him. End quote.
To sum up: it is permissible for the husband to give his zakaah to his ex-wife, if her ‘iddah has ended or it was an irrevocable divorce, if she is entitled to zakaah.