The carryover system has been recently revamped, allowing you to fight Guild Bosses with your other teams in spite of holding carryover time from a defeated boss.
You may now hold three separate instances of Carryover Time (one per team) With this change, the interface has also been slightly updated.
In order to access your carryover team, you will need to use the right or left arrows in the party selection screen to shuffle between your teams until you are selecting your desired Carryover Team. This will be indicated by the number of the team being Green in color. Once you have your Green color (carryover) team selected you can use it.