You roughly have 1 minute to take your turn.
Earlier turns it’s a little shorter than that; later turns a little longer than that

How much time you have can be seen as a timer-bar on the “End Turn” button in the bottom right.

When you are almost out of time, the screen will glow red.

If you don’t press End Turn, the turn will auto-end after you run out of time!  All of the actions that you have taken, if any, will lock in and play for that turn.