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