Can you ready an already readied Irelia?

No, you cannot ready an already readied Irelia, Fervent.

According to Rule 415.1.b of the Riftbound Core Rules: "A Unit that is already Ready cannot be Readied again." Additionally, Rule 415.1.c states: "If a Unit is instructed to be Readied while it is already Ready, nothing additional happens."

Because Irelia's triggered ability requires her to be successfully "readied" (or chosen) to gain the +1 Might bonus, if she is already in a Ready state, any effect that instructs you to ready her will fail to do so, and her ability will not trigger.