The Kabul valley and the region of Gandhara to the west of Indus came under the Achaemenid rule during the reign of Cyrus the Great (600–530 BCE).
Jointly, the region was known by its Iranian name Paruparaesanna as well as the Indian name Gandara.
It was administered at first from Bactria, but organised into a separate satrapy in c. 508 BCE with a headquarters possibly at Pushkalavati (near present-day Charsadda in Pakistan).
It was a tribute-paying region until the time of Artaxerxes (424 BCE), but it remained part of the royal conception of the empire until Alexander's conquest (c. 323 BCE).
At Alexander's time, the region was said to be governed by hyparchs (rulers in their own right, but professing subjection to the emperor).
The nature of the local administration under the Achaemenid empire is uncertain.
Magee et al.
note that neither the Achaemenid nor classical sources mention the presence of any satraps in Gandara.
However, there were official personages encountered by Alexander's companions.

Coinage was developed by the Greeks of the Asia Minor, influenced by the Lydian coinage in the 7th century BCE.
Over the next two centuries, the use of coins spread throughout the Mediterranean area.
 The Achaemenid conquest of Asia minor in 540 BCE made no immediate difference to the situation: the Greek coinage continued under the Achaemenid rule and the Iranian heartland itself had little use for money.
Daris I introduced new Achaemenid coins, gold darics and silver sigloi, primarily as replacements for the Lydian coins in the Asia minor.
While the darics proved to be popular, the sigloi did not catch on.
The Greek cities continued to mint their own silver coins.
A mix of these Greek silver coins and the Achaemenid sigloi thus began to circulate throughout the Achaemenid empire, the Greek coins generally being in a majority.
The Kabul valley and the region of Gandhara to the west of Indus came under the Achaemenid rule during the reign of Cyrus the Great (600–530 BCE). Jointly, the region was known by its Iranian name Paruparaesanna as well as the Indian name Gandara. It was administered at first from Bactria, but organised into a separate satrapy in c. 508 BCE with a headquarters possibly at Pushkalavati (near present-day Charsadda in Pakistan). It was a tribute-paying region until the time of Artaxerxes (424 BCE), but it remained part of the royal conception of the empire until Alexander's conquest (c. 323 BCE). At Alexander's time, the region was said to be governed by hyparchs (rulers in their own right, but professing subjection to the emperor). The nature of the local administration under the Achaemenid empire is uncertain. Magee et al. note that neither the Achaemenid nor classical sources mention the presence of any satraps in Gandara. However, there were official personages encountered by Alexander's companions.
Coinage was developed by the Greeks of the Asia Minor, influenced by the Lydian coinage in the 7th century BCE. Over the next two centuries, the use of coins spread throughout the Mediterranean area.  The Achaemenid conquest of Asia minor in 540 BCE made no immediate difference to the situation: the Greek coinage continued under the Achaemenid rule and the Iranian heartland itself had little use for money. Daris I introduced new Achaemenid coins, gold darics and silver sigloi, primarily as replacements for the Lydian coins in the Asia minor. While the darics proved to be popular, the sigloi did not catch on. The Greek cities continued to mint their own silver coins. A mix of these Greek silver coins and the Achaemenid sigloi thus began to circulate throughout the Achaemenid empire, the Greek coins generally being in a majority.
Kabul hoard