This phrase implies significant changes are anticipated with the arrival of the new person. When the new director started, everyone knew that as a new broom, he would revamp the entire department.
Pro Tip 2/3
Metaphorical Use
'A new broom' is a metaphor for someone who cleans up or makes improvements. Our team was underperforming, but the new coach is a new broom ready to sweep away bad habits.
Pro Tip 3/3
Context Sensitivity
The phrase is best used in contexts involving changes in an organization or group. The school hadn't won a championship in years, so the new principal was seen as a new broom.