Consider the description of Yosef when he was appointed to the position of second to the king. As the Prime Minister, Mordechai (like Yosef) would be required to wear the garments appropriate to his position. The question should be why Mordechai did not start wearing the appropriate garments once the need for sak ve'eifer was over (after Purim). After the initial time (when he had to wear royal garments by command of the king), he resumed his mourning garments. Thus the answers cited below, show why he did not dress in royal garments until then.
Esther 8:8 shows that this is the time when Mordechai was actually given the authority to issue decrees in the name of the king and sealed with the king's ring.
And you-write about the Jews as you see fit, in the name of the king,
and seal [it] with the king's ring, for a writ that is written in the
name of the king and sealed with the king's ring cannot be rescinded."
Malbim on Esther 8:5 says
שמרדכי יצא להודיע צדקת מרדכי שלא קבל על עצמו שום גדולה עד שנכון לבו
בטוח שהיתה אורה ותשועה לאחיו האומללים שאז יצא בלבוש מלכות לא קודם
Mordechai refrained from dressing as befitted his (now royal) position until he had been able to complete the saving of the Yehudim and they could rejoice.
The Chachmei Tzorfas there point out that the language is specifically set up to parallel the mourning when the original decree was issued and contrast what Mordechai wore then.
ומרדכי יצא מלפני המלך – במקום: ויצא בתוך העיר (אסתר ד׳:א׳) ויצעק צעקה.
בלבוש מלכות – במקום: וילבש שק ואפר (אסתר ד׳:ב׳). ועטרת זהב גדולה
ותכריך בוץ וארגמן – ובמקום: העיר שושן נבוכה (אסתר ג׳:ט״ו): והעיר שושן