““He shall remove his garments and wear other garments and he shall take out the ashes.”
~ Leviticus 6:4

The first daily Temple-service was the removal of the previous day’s ashes from the Altar.

Why did the priest need to change clothes?

Sorry budding Kabbalists, no hidden mysticism here and not even a mitzvah! Rather just simple commonsense: sense he’s likely to soil his holy garments from the dirty ashes, the priest should change into ‘overalls’. Evidently, certain clothing is unsuitable for specific pursuits.

If you dress appropriately for business-meetings or social-functions, why should spiritual ones be any different?