The السنة at عرفة is to combine Dhuhr and Asr الصلوات at the time of Dhuhr (early combination, or jam' taqdim). Both الصلوات are shortened to 2 ركعةs each since the الحاج is considered a traveler. النبي (صلى الله عليه وسلم) performed them with one adhan and two iqamas — meaning one call to الصلاة is given, then Dhuhr is prayed with its own iqama, followed immediately by Asr with its own iqama. No voluntary الصلوات (السنة الصلوات) are prayed between them.
This combining serves an important practical purpose: it frees up the entire afternoon from after the الصلوات until sunset for uninterrupted دعاء, dhikr, and worship — the core purpose of the Day of عرفة. The afternoon hours are the most precious time of the entire الحج and should not be interrupted by waiting for the Asr الصلاة time.
Regarding who should combine: the majority of scholars say all الحجاج at عرفة combine, even residents of مكة who are not technically travelers. The combining is specifically linked to the الحج ritual at عرفة, not just to the traveler's concession. The same principle applies at مزدلفة, where Maghrib and Isha are combined at Isha time (jam' ta'khir — delayed combination). After the combined الصلاة at عرفة, face the القبلةh, raise your hands, and dedicate yourself fully to الدعاء.