Yudhisthira had the same question to Markandeya.
This is what Kalki will do before another Satya Yuga begins.
And commissioned by Time, a Brahmana of the name of Kalki will take his birth. And he will glorify Vishnu and possess great energy, great intelligence, and great prowess. And he will take his birth in a town of the name of Sambhala in an auspicious Brahmana family. And vehicles and weapons, and warriors and arms, and coats of mail will be at his disposal as soon as he will think of them. And he will be the king of kings, and ever victorious with the strength of virtue. And he will restore order and peace in this world crowded with creatures and contradictory in its course. And that blazing Brahmana of mighty intellect, having appeared, will destroy all things. And he will be the Destroyer of all, and will inaugurate a new Yuga. And surrounded by the Brahmanas, that Brahmana will exterminate all the mlecchas wherever those low and despicable persons may take refuge."
He will later conduct a horse sacrifice.
"Markandeya continued, 'Having exterminated the thieves and robbers, Kalki will, at a great Horse-sacrifice, duly give away this earth to the Brahmanas, and having established anew the blessed rectitude ordained by the Self-create, Kalki, of sacred deeds and illustrious reputation, will enter a delightful forest, and the people of this earth will imitate his conduct, and when the Brahmanas will have exterminated the thieves and robbers, there will be prosperity everywhere (on earth). And as the countries of the earth will one after another be subjugated, that tiger among Brahmanas, Kalki, having placed deer skins and lances and tridents there, will roam over the earth, adored by foremost Brahmanas and showing his regard for them and engaged all the while in slaughtering thieves and robbers. And he will exterminate the thieves and robbers amid heart-rending cries of 'Oh, father--' 'Oh, mother!--'O son!' and the like, and O Bharata, when sin will thus have been rooted out and virtue will flourish on arrival of the Krita age, men will once more betake themselves to the practice of religious rites.
Kalki will exerminate thieves, robbers, mlecchas wherever those low and despicable humans may take refuge. The sin will be rooted out and virtue will flourish on arrival of the Krita age.