The person everyone comes to a mutual agreement about to be the manager of the country is the Prime Minister.

Compared to 首相 or 総理大臣 that you've learned as "prime minister" previously, 宰相 were prime ministers appointed by monarchs. So this is a bit of a dated term used for the prime ministers of an imperial or royal court.

This is a jukugo word that uses the on'yomi readings of the kanji. You already know both readings, but make sure to read 相 as しょう. This should be easy to remember since Shoguns (しょう) were like prime ministers back in the day!