Islamqa.org says it's tazir:

Bestiality is absolutely unlawful and a major crime in Islam. This needs no explanation.

The tradition related by Ibn `Abbas merely affirms that there is no penal punishment for the act. There are very few specifically prescribed penal punishments. However, in the event that such an act occurs, the perpetrator would be punished as per the discretion of the government.

But Islamweb says the punishment is death:

Bestiality is a grave sin and a reprehensible misdeed. Allaah, The Exalted, says (what means): {And do not approach immoralities – what is apparent of them and what is concealed.} [Quran 6:151] The Prophet , said: "Cursed is he who curses his father; cursed is he who curses his mother; cursed is he who dedicates an animal sacrifice to other than Allaah; cursed is he who meddles with the borders of someone's land (unjustly alters the landmark to encroach upon that land); cursed is he who misleads a blind person away from his path; cursed is he who has intercourse with an animal; cursed is he who does the act of the people of Loot (sodomy)." [Ahmad - Al-Arnaa’oot said its Isnaad (chain of narrators) is Hasan (good)]

The Prophet , also said: "If someone engages in sexual intercourse with an animal, kill him and kill the animal." [Ahmad and others - Al-Arnaa’oot said its Isnaad is Hasan]

What is the punishment of bestiality in Islam?