From my searches, the Tanach does not have the term Psak or Posek in it. Many questions here related to questions on psak quote the Rambam, but those sections refer to Horyaot, or Divrei Halacha, or Shalot V'T'shuvot.
When did the term Posek and Psak start to get used? Why did the language change?
For example, there is the collection of Midrashim known as Psikata Rabahti. But these are statements of agadatah not halacha and are not rulings.
Then, later in the Rambam, he makes a refernce to a "Psak Din", made by a "Baalai dinin". Which is closer to the way the term is used today, but not exactly the same still, especially since it's referring to an actual court:
י [ח] שָׁאַל אֶחָד מִבַּעֲלֵי דִּינִין לִכְתֹּב לוֹ פְּסַק דִּין, כּוֹתְבִין לוֹ כָּךְ--בָּא פְּלוֹנִי לְבֵית דִּין שֶׁלִּפְלוֹנִי עִם פְּלוֹנִי בַּעַל דִּינוֹ, שֶׁטְּעָנוֹ בְּכָּךְ, וְיָצָא זַכָּאי, אוֹ חַיָּב; וְנוֹתְנִין לוֹ. וְאֵין מַזְכִּירִין שֵׁם הַמְּזַכִּין וְלֹא שֵׁם הַמְּחַיְּבִין, אֵלָא בֵּית דִּינוֹ שֶׁלִּפְלוֹנִי, מִדִּבְרֵיהֶם נִזְכָּה פְּלוֹנִי.
**This is not a question about etymology.