Is it normal that a virtual BIG-IQ uses almost 7ghz from a esxi host.
Also the cpu is always at around 80-85 % if I check the cpu under monitor on the server itself.
Its only used to manage licenses and not BIG-IP systems so it should idle most of the time.
Check the cpu with the linux top command to see which process is causing the issue and upload a gkview to ihealth. This issue needs you to do basic investigation.
Could you tell us the configuration of your VM and version of BIG IQ?
Because the recommendation is to use 32GB RAM, and 8vCPU, since v7.1
I understood that you are using just with License Manager but...