The Sunnah at Arafah is to combine Dhuhr and Asr shalat at the time of Dhuhr (early combination, or jam' taqdim). Both shalat are shortened to 2 rak'ahs each since the jamaah haji is considered a traveler. Nabi (shallallahu alaihi wa sallam) performed them with one adhan and two iqamas — meaning one call to shalat is given, then Dhuhr is prayed with its own iqama, followed immediately by Asr with its own iqama. No voluntary shalat (Sunnah shalat) are prayed between them.
This combining serves an important practical purpose: it frees up the entire afternoon from after the shalat until sunset for uninterrupted doa, dhikr, and worship — the core purpose of the Day of Arafah. The afternoon hours are the most precious time of the entire Haji and should not be interrupted by waiting for the Asr shalat time.
Regarding who should combine: the majority of scholars say all jamaah haji at Arafah combine, even residents of Mekkah who are not technically travelers. The combining is specifically linked to the Haji ritual at Arafah, not just to the traveler's concession. The same principle applies at Muzdalifah, where Maghrib and Isha are combined at Isha time (jam' ta'khir — delayed combination). After the combined shalat at Arafah, face the Qiblah, raise your hands, and dedicate yourself fully to doa.