They can also look at Antonio Conte who is vacant. He is a good tactician and will help these talented players.
Conte would absolutely be a great choice. Maybe even the best one. Because as you know Conte already has a history with Chelsea. He made Chelsea Premier League and FA Cup champions once each.

While he is available why don't they just go for him first? If I were Chelsea chairman my priority would be to do that. However I haven't even heard his name among those many rumours. I just want to see them finding a decent manager and not giving up on him easily just as they did with Pochettino.

This isn't the road going to success for sure. Patience is one of the most important factors in football. It hasn't been easy for most top teams to reach this level.
Conte is likely to move to Napoli after a long break, Chelsea doesn't seem to have included Conte on the list of coaches they are targeting. After officially parting ways with Pochettino, several names are now being linked as potential Chelsea coaches next season. In fact, Chelsea fans still hope that the club owner will retain Pochettino, even though a small number think otherwise. To compete to become a team challenging for the title next season, it is clear that Chelsea management must look for a quality coach who has experience coaching Premier League clubs, because it speeds up adaptation and has a quick impact on the club development.
Meanwhile, Chelsea decision to fire Pochettino indicates that club officials and management are impatient, even though Pochettino never got the full opportunity to show his best tactical qualities this season, because most of Chelsea players took turns in the treatment room due to injuries. With Chelsea young squad already developing, perhaps next season it will be easier to compete in the top four of the standings if Pochettino still stays, but Chelsea journey will be continued by different people. Of course, no success is easy to achieve, now Chelsea position is quite risky if they rashly appoint a new coach.