I love the KJV. Sometimes, however, it uses terms or phrases that are archaic or otherwise hard to understand. One of those expressions is "keep under." The expression appears twice:
2 Chronicles 28:10 And now ye purpose to keep under the children of Judah and Jerusalem for bondmen and bondwomen unto you: but are there not with you, even with you, sins against the LORD your God?
1 Corinthians 9:27 But I keep under my body, and bring it into subjection: lest that by any means, when I have preached to others, I myself should be a castaway.
In both instances the expression means "to subdue." Today we might use the similar expression "hold down."