Fasting on the Day of Arafah (the 9th of Dzulhijjah) is one of the most virtuous voluntary fasts in Islam for those who are not performing Haji. Nabi (shallallahu alaihi wa sallam) was asked about fasting on the Day of Arafah and said: 'It expiates the sins of the previous year and the coming year.' This tremendous reward makes it one of the most highly sunnah acts of worship for non-jamaah haji.
However, jamaah haji who are actually at Arafah performing Haji are advised NOT to fast on this day. Nabi (shallallahu alaihi wa sallam) himself did not fast on the Day of Arafah during his Haji. The reason is practical and spiritual — the Day of Arafah requires immense physical and spiritual energy. Pilgrims are standing in extreme panas for hours, making intense doa-doa, and need their strength. Fasting could compromise their ability to worship fully. There was even a narration where Umm al-Fadl sent a container of milk to Nabi at Arafah, and he drank it publicly to show people he was not fasting.
For non-jamaah haji around the world, this fast is separate from the Days of Tashreeq (11th-13th Dzulhijjah), on which fasting is prohibited. The Day of Arafah fast is standalone and carries its immense reward independently. Combined with increased dhikr, doa, and charity on this day, non-jamaah haji can spiritually participate in the blessings of the Haji season from wherever they are.