Most automation systems will automatically handle this by repeating the 1 am hour. Check with technical support for your automation vendor. In Natural Log, simply create a 1 AM hour with double the normal number of breaks [if any] in the 1 AM hour. It is recommended you put no time-specific automation commands in the 1 AM hour as this will likely foul up the automation system.

If you are merging with music, you should create a special 1AM clock with twice as much music as a normal. In other words, if you normally schedule 22 songs per hour, in that one hour schedule 44 songs.

When Daylight Saving Time begins in the spring:

Most automation systems will automatically handle this by skipping the 2 a.m. hour.

It is very important that you empty your logs of any items in the 2 a.m. hour, since these will not play.
You must also be sure not to have any timed events during the 2 a.m. hour.