For an IT pro today the (not so)new era of the cloud is not that different from the on premise world.
Cloud is built on the premise of not having to worry about the day to day underlying infrastructure. You don't have to worry about power, hardware etc. You do however need to worry about networking, security, performance just like an on premise environment.
As an IT pro today the skills that you have learnt previously will mainly still apply to the cloud world. Take networking for example. An Azure implementation still relies on basic networking concepts like sub nets etc to work so the IT pro still needs to understand these basic technologies. There is now just much more power in the networking stack. Things like micro segmentation build on what was available using VLAN's to configure and secure your cloud environment but the core concepts are the same.
Security is still just as important in the cloud as on premise but IT pro's can use the same skill sets used in the on premise world in the cloud. Most of the major firewall vendors provide virtual versions of their hardware devices so that the cloud environment becomes just another location that they manage.
IT pro's will still need to monitor the performance of the servers under their watch but they will increasingly need to monitor PaaS applications like Azure SQL Database or App Service. The good news is the tooling provided by default is streets ahead of what was available and improving all the time. The ability to use analytics to monitor log files and provide the right information without overloading the IT pro is a game changer that I wish we had when I got into IT.
To stay relevant the IT pro needs to complement their existing skills with cloud skills and they will be on a path to lifelong IT career.