I have a broken water pipe on the main water line coming into the house, just before the main water valve. Can any license plumber repair this problem or do I have to notify the city to have this pipe repaired? Approximately how much will it cost to be repaired?

Any licenced plumber can fix it as long as it is your property and you own the line that is leaking, the cost will depend on what type of waterline is leaking, and how accessible the line is. If the waterline is plastic it may be an easy fix, if its galvanized and corroded it could end up being a temporary fix, worst case you may have to replace the whole yardline, a licenced plumber hourly rates very, call your local plumbing co. and ask for a quote to do the repairs. Good luck on this matter.

You should notify your city water department of the leak. It is very likely that you do own the main and will be responsible for the repairs but it is worth checking. The repair may require the city to shut down the main from their end and they usually don't like it when anyone other than them touches their valve.

I live in an area where just recently the city must turn on and off the water. Previously a licensed plumber could do it.

If you live out of this particular city, a plumber or a homeowner can do it. If a homeowner does it, they put down a deposit and then pick up and return the required two tools.