Perhaps there is an explanation, but I can’t find it in the rulebook. I’ve just taken a star (from a quitted player), but it won’t let me build a new carrier. (I can at my two other stars, but that would cost significantly more time).
What about a new heading along these lines for the “Hyperspace Carriers” entry in the Codex:
Building Carriers
A carrier may be built on any star which has at least one ship available to become flagship of the new fleet. When a carrier is built, this first ship is automatically transferred from the star’s garrison to the carrier.