The Sunnah at Arafat is to combine Dhuhr and Asr prayers at the time of Dhuhr (early combination, or jam' taqdim). Both prayers are shortened to 2 rak'ahs each since the pilgrim is considered a traveler. The Prophet (peace be upon him) performed them with one adhan and two iqamas — meaning one call to prayer is given, then Dhuhr is prayed with its own iqama, followed immediately by Asr with its own iqama. No voluntary prayers (Sunnah prayers) are prayed between them.
This combining serves an important practical purpose: it frees up the entire afternoon from after the prayers 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 Hajj and should not be interrupted by waiting for the Asr prayer time.
Regarding who should combine: the majority of scholars say all pilgrims at Arafat combine, even residents of Makkah who are not technically travelers. The combining is specifically linked to the Hajj ritual at Arafat, 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 prayer at Arafat, face the Qiblah, raise your hands, and dedicate yourself fully to supplication.