If you talk about Liverpool's patience with Klopp, then I think it's because they showed respect for him because of the titles they won in previous seasons, and Klopp in subsequent seasons ensured that the team was revived, and moved towards new victories. Klopp's strength was that he would get his players to give their all on the field, and I think it's impossible to play like that season after season, so it was logical that after a great season there would be a decline. I don’t know how patient Liverpool will be with new coaches who haven’t achieved anything yet.
A team like Liverpool is a team that has already make name in the Premier League; they were patient with Jurgen Klopp and he tried his best when he joined them from Dortmund to bring glory back to the team and he did, I think it was his last two seasons that things didn't go well with him which was he left before been sacked; but he did a wonderful job for the team and signed great players to give the fans great memories.
Arne Slot is coming from another League that is nit as tough as the Premier League, therefore, Liverpool fans and management needs to be patient with him before he will adapt to the Premier League style of play, and also I am sure some important players will leave the team, so he need time to rearrange the team to his taste so as to get the best performance the team need. I don't expect him to give a better performance this season, but a season after this one will be tough.