A proverb says a new broom
I think I know this one!
The proverb is: "A new broom sweeps clean, but an old broom knows all the corners."
This means that a new person or thing (like a new broom) may be effective at first, but an old one (like an old broom) has experience and knows all the hidden spots and corners that need attention.
But I think you might be thinking of a different proverb: "A new broom sweeps clean, but an old broom knows where to sweep." This one suggests that a new person or thing may be enthusiastic and effective at first, but an old one has learned where to focus their efforts and has a deeper understanding of what needs to be done.
Do either of these sound like the proverb you were thinking of?