9:19a Shallum son of Kore, the son of Ebiasaph, the son of Korah,

Shallum’s ancestors were Kore, Ebiasaph, Korah, ⌊and Levi⌋ .
-or-
Shallum’s father was Kore. Kore’s father was Ebiasaph. Ebiasaph’s father was Korah. ⌊Korah was a descendant of Levi.⌋

9:19b and his relatives from the Korahites

Shallum and his family were from Korah’s clan. They were gatekeepers/doorkeepers.
-or-
So Shallum and his relatives were from the clan of Korah.

9:19c were assigned to guard the thresholds of the Tent

Their duty/responsibility was to guard the gates/doors of the tent/temple.
-or-
They guarded the entrances/gates to the tent/house ⌊of Yahweh in Jerusalem city⌋ .

9:19d just as their fathers had been assigned to guard the entrance to the dwelling of the LORD.

In the same way, their ancestors had also had the duty/responsibility to guard the gates/doors to the tent/temple of Yahweh ⌊in the Israelite camp⌋ .
-or-
They continued the work/service of their ancestors. ⌊Their ancestors were the ones⌋ who were responsible for guarding the entrance/gate to the house/tent of Yahweh ⌊in the wilderness/desert⌋ .

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