I'm playing this agenda (when I would claim or move power to my house, I must place it on one of my Brotherhood characters), but I have no Brotherhood character in play (nor a character with Infamy). What happens if I win a power challenge (with non-zero claim)? Does my opponent keep his power or is it lost?

The prize for winning a power challenge is to move power from your opponent's House to yours. It's a single, all-or-nothing effect. If you have nowhere to move it "to" because of the Brotherhood Agenda, you never move it "from" anything, either. Your opponent keeps their power.

The important thing to remember is that the prize for winning a power challenge is a single redistribution of the power on the board. It is not a two-step process of discarding it from one place and claiming it in another.

Thanks for the answer