Here "kingdom" stands for God's rule as king. AT: "to whom I preached the message about God's reign as king" or "to whom I preached about how God will show himself as king" (See: [[rc://en/ta/man/translate/figs-metonymy]])
# will see my face no more
The word "face" here represents Paul's physical body. AT: "will not see me anymore on this earth" (See: [[rc://en/ta/man/translate/figs-synecdoche]])