Living Rules Reference · v2.0
4
Active Player
The active player is the player taking a turn during the action phase.
During the action phase, the player who is first in initiative order is the first active player.
After the active player takes a turn, the next player in initiative order becomes the active player.
After the last player in initiative order takes a turn, the player who is first in initiative order becomes the active player again, and turns begin again in initiative order, ignoring any players who have already passed.
Source: Twilight Imperium: Fourth Edition — Living Rules Reference v2.0 (September 22, 2020), page 9. Rules text reproduced verbatim; the rulebook’s diagrams are omitted.