Captaincy is the job of being captain, or the stretch of time while someone is captain. You hear it most in sport: if she took the captaincy in 2024, she became the team captain then. During her captaincy means in the years she held that job. It is a slightly newspaper kind of word. On the playground, children just say “She’s the captain.” Adults writing about football or baseball like captaincy because it names the role as a thing you can win, lose, or pass on. Though actually, you can use it for a ship’s captain or an army captain too, but everyday talk then more often says command or “his time as captain.”