Liverpool Arne Slot, have had quite a good starting of the season both in the Premier league game and in the European competition, however from the perspective of him being a new coach and first time managing Liverpool football club, not every new coach will start off this way in their first, where most of the newly signed coaches use their first season to experiment tactical system that will work.
I think Arne Slot is a little bit different. Most managers usually replace old managers because they can't give good results for their clubs. The team is in bad form and the new manager has to experiment to get good tactics. This is different from Liverpool where last season Liverpool was one of the title contenders and Klopp was not fired but decided to retire because he wanted to take a break from football. Arne Slot just needed to do some improvisation and luckily Arne Slot was able to immediately get the chemistry that made Liverpool appear very solid this season.