The word "permission" can be stated as a verb. Alternate translation: "the captain permitted Paul to speak" or "the captain allowed Paul to speak" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
It can be stated explicitly why Paul motioned with the hand. Alternate translation: "motioned with his hand for the people to be quiet" (See: [[rc://en/ta/man/translate/figs-explicit]])