Question: Between 681 and 669 BC, around the time Kaus-gabri ruled Edom, who was the King of Assyria?

Context paragraphs:
Tarshish: Tarshish (Hebrew: תַּרְשִׁישׁ‎ ‎ ) occurs in the Hebrew Bible with several uncertain meanings, most frequently as a place (probably a large city or region) far across the sea from the Land of Israel and Phoenicia (Tarshish is currently the name of a village in Mount Lebanon District in Lebanon).  Tarshish was said to have supplied vast quantities of important metals to Israel and Phoenicia.  The same place-name occurs in the Akkadian inscriptions of Esarhaddon (the Assyrian king, d. 669 BC) and also on the Phoenician inscription on the Nora Stone; its precise location was never commonly known, and was eventually lost in antiquity.  Legends grew up around it over time so that its identity has been the subject of scholarly research and commentary for more than two thousand years.  Its importance stems in part from the fact that Hebrew biblical passages tend to understand Tarshish as a source of King Solomon's great wealth in metals - especially silver, but also gold, tin and iron (Ezekiel 27).  The metals were reportedly obtained in partnership with King Hiram of Phoenician Tyre (Isaiah 23), and the fleets of Tarshish-ships.  However, Solomon's Temple was destroyed by the Babylonians, thus archaeological evidence has been difficult to uncover.

Sennacherib: Sennacherib (Akkadian: Sîn-ahhī-erība, "Sîn has replaced the brothers"; Syriac: ܣܝܢܚܪܝܒ‎ , "Sīnḥārīḇ " ; Hebrew: סַנְחֵרִיב‎ ] ] ) was the king of Assyria from 705 BCE to 681 BCE.  He is principally remembered for his military campaigns against Babylon and Judah, and for his building programs – most notably at the Akkadian capital of Nineveh.  He was assassinated in obscure circumstances in 681 BCE, apparently by his eldest son (his designated successor, Esarhaddon, was the youngest).

Adad-shuma-usur: Adad-šuma-uṣur, inscribed , meaning "O Adad, protect the name! ," and dated very tentatively ca. 1216–1187 BC (short chronology), was the 32nd king of the 3rd or Kassite dynasty of Babylon and the country contemporarily known as Karduniaš.  His name was wholly Babylonian and not uncommon, as for example the later Assyrian King Esarhaddon (681–669 BC) had a personal exorcist, or "ašipu", with the same name who was unlikely to have been related.  He is best known for his rude letter to Aššur-nirari III, the most complete part of which is quoted below, and was enthroned following a revolt in the south of Mesopotamia when the north was still occupied by the forces of Assyria, and he may not have assumed authority throughout the country until around the 25th year of his 30-year reign, although the exact sequence of events and chronology remains disputed.

Esarhaddon: Esarhaddon (Akkadian: "Aššur-aḥa-iddina" "Ashur has given a brother"; Hebrew: אֵסַר חַדֹּן‎ ‎ ; Ancient Greek: "Ασαρχαδδων" ; Latin: "Asor Haddan" ) was a king of the Neo-Assyrian Empire who reigned 681 – 669 BC.  He was the youngest son of Sennacherib and the West Semitic queen Naqi'a (Zakitu), Sennacherib's second wife.

Ruda (deity): Ruda is a deity that was of paramount importance in the Arab pantheon of gods worshipped by the North Arabian tribes of pre-Islamic Arabia.  The etymology of his name gives the meaning "well disposed" an indication of his function as a protective deity.  The oldest reference to Ruda is found in the annals of Esarhaddon who ruled over the Assyrian empire from 681 to 669 BC.  The name is transliterated into Latin script from the original Akkadian as "Ru-ul-da-a-a-ú" and he is mentioned among the gods of the Arabs.  Known as Arsu among the Palmyrans, in a later Aramaic inscription, Arsu/Ruda is paired with the Syrian god Resheph, a protective deity for his worshippers from the 3rd millennium BC.

Assyria: Assyria was a major Mesopotamian kingdom and empire of the ancient Near East and the Levant.  It existed as a state from perhaps as early as the 25th century BC in the form of the Assur city-state, until its lapse between 612 BC and 599 BC, spanning the Early to Middle Bronze Age through to the late Iron Age.  From the end of the seventh century BC to the mid-seventh century AD, it survived as a geopolitical entity, for the most part ruled by foreign powers, although a number of Neo-Assyrian states arose at different times during the Parthian and early Sasanian Empires between the mid-second century BC and late third century AD, a period which also saw Assyria become a major centre of Syriac Christianity and the birthplace of the Church of the East.

List of Mesopotamian dynasties: Base on an Assyria record of Eclipse on June 15, 763 BC, and the related date documents between Assyria and Babylonia, the dates after 1400 BC are reliable.  According to the Venus tablet of Ammisaduqa, a record of astronomical observations of Venus in Old Babylonian Empire king Ammisaduqa (1646–1626 BC), the rough date can be concluded.  But about the accuracy date, the Historians have different opinions, in high chronology the finish date of Old Babylonian is 1651 BC, in middle chronology the finish date of Old Babylonian is 1595 BC，and in low chronology the finish date of Old Babylonian is 1531 BC.  In this article we use the middle chronology, same as most of the books about Mesopotamia, but there are many evidence support the low chronology (even extreme low chronology).

Kaus-gabri: Ḳaus-gabri was king of "Udumi" or Edom in the 680s BC, during the reign of the Assyrian king Esarhaddon.  His name may mean "[the god] Kaus is my champion".

Ushpia: Ushpia was an early Assyrian king who ruled Assyria ("fl. " "c." 2030 BC), as the second last within the section "kings who lived in tents” of the Assyrian King List (AKL), however; Ushpia has yet to be confirmed by contemporary artifacts.  According to the "Cambridge Ancient History", the conclusion of this section, "marked the end of the nomadic period of the Assyrian people," and, "visualized Ushpia as the actual founder of the Semitic city of Aššur."  Ushpia is alleged to have founded the temple for the god Aššur within the city-state of Aššur, according to the much later inscriptions of both of these Assyrian kings: Shulmanu-asharedu I ("fl. " "c." 1274 BC) and Aššur-ahu-iddin ("fl. " 681 BC).  Ushpia is succeeded on the AKL by Apiashal.  Arthur Ungnad interpreted both Ushpia's and Kikkia's ("fl. " "c." 2000 BC) names as being that of the Hurrian language (as opposed to the Assyrian dialect of the Semitic Akkadian language), but; Arno Poebel was not convinced by this interpretation and more recent research no longer holds Ungnad's thesis as tenable.

Esarhaddon's Treaty with Ba'al of Tyre: Esarhaddon's Treaty with Ba'al is an Assyrian clay tablet inscription describing a treaty between Esarhaddon (reigned 681 to 669 BC) and Ba'al of Tyre.  It was found in the Library of Ashurbanipal.

Supporting paragraphs: Kaus-gabri Esarhaddon
Answer: Esarhaddon