Is it a requirement for performing the Sunnah of Asr prayer that it be observed between the Adhan and the Iqamah, or is it permissible to perform it thereafter?

It is permissible to perform the Sunnah Rawatib (regular voluntary prayers) before the Asr prayer at any time the prayer is performed, and it is not a condition that this be between the adhan (call to prayer) and the iqama (second call to prayer initiating the prayer). However, it is not permissible to be preoccupied with them if there is a fear of the prayer time expiring and the obligatory prayer being missed. It is preferable to perform the prayer at the beginning of its time.