Missing the standing at Arafat entirely means the pilgrim has missed Hajj, as the Prophet (peace be upon him) said: 'Hajj is Arafat.' If a pilgrim fails to be present at Arafat at any point between the afternoon (zawal) of the 9th and dawn (fajr) of the 10th of Dhul-Hijjah, their Hajj is not valid and cannot be completed that year. This is the unanimous position of all four schools of jurisprudence.
Sheikh Ibn Baz explained the procedure for someone who has missed Arafat: the pilgrim should convert their intention to Umrah, perform tawaf around the Ka'bah and sa'i between Safa and Marwah, cut or shave their hair, and exit the state of ihram. This converts their missed Hajj into an Umrah, which releases them from ihram. If the Hajj they missed was their obligatory (first) Hajj, they must perform it the following year.
Sheikh Ibn Uthaymeen added that if the missed Hajj was a voluntary Hajj, there is no obligation to make it up. He also noted that a dam (sacrifice of a sheep) is required according to the Hanafi and Maliki schools for someone who missed Hajj and converted to Umrah, while the Shafi'i and Hanbali schools do not require a dam for the conversion itself. The key lesson is the absolute centrality of Arafat to the Hajj — without it, no other rite can substitute or compensate.