When using Darkrai VSTAR's "Star Abyss" Ability, can I use the Ability first, and then later put 2 Item cards into my hand?
No, you must take the 2 Item cards immediately when using Star Abyss. "During your turn" simply means you cannot use this Ability multiple times during the same turn.
Source: Astral Radiance FAQ; TPCi Rules Team (2022-05-26)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH10_99
SWSH10_99