Grading: This hadith is sahih, and this particular chain is "hasan".
Technical note / Defect ('illah): There is disagreement over Hisham bin Urwah in the chain of this narration, the details of which we have given in "Musnad Ahmad".
Reference / Source: Imam Ahmad recorded it 33/(20357) from Abd Allah bin Numayr, and Ibn Hibban (5689) via Amr bin al-Harith; both of them narrate it from Hisham bin Urwah with this same chain.

Reference / Source: Imam Ahmad recorded it 38/(23163) via Zuhayr bin Mu'awiyah, from Hisham bin Urwah, from his father (Urwah bin al-Zubayr), from al-Ahnaf bin Qays, that a paternal uncle of al-Ahnaf came to the Messenger of Allah (peace and blessings be upon him).
Note / Clarification: In this narration his uncle's name is not mentioned (i.e. he is left unnamed).

Reference / Source: Imam Ahmad recorded it 25/(15964) and 33/(20358), and Ibn Hibban (5690), via Yahya bin Sa'id al-Qattan from Hisham bin Urwah, in which al-Ahnaf's uncle is named "Jariyah bin Qudamah", that a man said: O Messenger of Allah! Give me some advice.
Technical note / Defect ('illah): In his narration Yahya al-Qattan added an (extra) person between Jariyah bin Qudamah and the Prophet (peace and blessings be upon him).

Reference / Source: Imam Ahmad recorded it 33/(20359) via Abu Mu'awiyah (Muhammad bin Khazim) from Hisham bin Urwah, in which Jariyah bin Qudamah says: "An uncle of mine told me that he came to the Messenger of Allah (peace and blessings be upon him)".
Technical note / Defect ('illah): Abu Mu'awiyah made it the hadith of Jariyah's uncle.

Reference / Source: Imam Ahmad recorded it 38/(23137) via Abu al-Zinad (Abd Allah bin Dhakwan), from Urwah bin al-Zubayr, from al-Ahnaf bin Qays, who said: "A cousin of mine told me: I said to the Messenger of Allah (peace and blessings be upon him)".
Technical note / Defect ('illah): In this narration he attributed it to his cousin and left his name unspecified.

Corroborating chains and supporting reports: On this topic there is the narration of Abu Hurayrah in Sahih al-Bukhari (6116), that a man said to the Prophet (peace and blessings be upon him): Advise me. He (peace and blessings be upon him) said: "Do not become angry." The man repeated his request several times, and each time he said: "Do not become angry."

General principle: Explaining the words "Do not become angry", Imam Ibn Hibban says: what is meant is that in a state of anger you should not do anything I have forbidden you; it does not mean that a person should never feel anger at all, because anger is part of human "jibillah" (innate nature), and it is impossible to forbid a person the nature upon which he was created. Hence the prohibition in this hadith is really directed at the acts that result from anger.