If a team is out of time-outs and an official grants a fourth time-out, what happens?

End the timeout and start the clock on the ready.

Is there a penalty?

No. Only in basketball.

The penalty is on the official who granted the timeout. :D

If this happened with only a few seconds on the clock then, if in your opinion, the clock would have run out before the ball would have been snapped then wind the clock without blowing the ball ready for play. Don't let the team who called the TO get an extra snap at the end of a period because of this.

Communication is very important here so that all officials know how many timeouts each team has and each team's coaches know how many they have left.

Only in the NFL.