This is one of the 23 delegations (satrapies) shown bringing offerings to the King during the New Year (Nou Rutz) festival.
The bas relief of each delegation provides valuable insight into the clothes and gifts from each region at that time.

The Median delegation are shown 7th from the left (1st on the right), on the top tier of the Apadana stairway.
The Medes lived in North Western Iran and were themselves a formidable power in that region before being conquered by Cyrus the Great in 550 BC.

They are represented by 9 members, and bring a pitcher, bowls, a sword (akinakes), rings, a cloak, a coat, and trousers.
Only the first Mede in the delegation is shown wearing the traditional round cap, the others are wearing turbans.

The original bas relief is shown in one of the photographs (with low tonal range due to the shade).
The other photographs have been digitally enhanced by blurring the background in order to reveal their otherwise hidden beauty. I hope you find them as fascinating as I do.

You can view the Mede delegate on the Tomb of Darius the Great at Naqsh-e Rustam using this link.