'A new brush sweeps clean' means that someone with a new perspective can make great changes. However, the full version is 'a new brush sweeps clean, but an old brush knows the corners', which warns that experience is also a valuable thing. Sometimes 'broom' is used instead of 'brush'.
This means that something is worthless and dates back to when someone would travel around the countryside repairing things such as a kitchen pot with a hole in it. He was called a 'tinker'. His dam was used to stop the flow of soldering material being used to close the hole. Of course his 'trade' is passť, thus his dam is worth nothing.