The music will be played softly when it is our turn to enter the ring determine the case and function of the underlined pronoun.
possessive; direct object
nominative; subject
objective; indirect object
possessive; adjective

The pronoun here is "our" in "our turn" ("it is our turn to enter the ring") - I see no other pronoun here.

This pronoun is a possessive pronoun ("our" is a possessive pronoun in general) and its function is to function as an adjective - it describes "turn")

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