I don't know this adage but google tells me that there's such version: nowa miotła dobrze zamiata ale stara wie, gdzie są śmieci. This would mean that eg. a person that is new to some place is eager to act and tries to do everything really well, but somebody who has been there for a while already knows how things work, knows more people and is better on these fields.

I think it's a (shortened) literal translation of "a new broom sweeps clean". You often hear it in sports when a coach is fired and the team wins the next game under a new one. The one Caliette mentioned means the total opposite :)