to have an up to date anti-virus installed.
The license for your current Trend Micro anti-virus may have expired but that will not stop it working. However, if it is not now updating it's virus definitions then you will need to consider your next steps.
1] Renew the license for Trend Micro, or
2] Purchase a new anti-virus, or
3] Go for one of the many free anti-virus applications available.
Since the license for your version of Trend Micro is expired that advert you see is probably a gentle reminder about that. it can either be hard-wired into the software itself, or Trend may be checking on the internet on startup.
When an internet capable computer is turned on, the network card connects to the internet very early on, even before Windows loads, so Trend could well be checking itself before Windows completes it's startup routine.
That's one reason why a firewall is so important. In that early stage of startup before Windows loads and any security applications are loaded up, the system is vulnerable. Most good firewalls have a component that loads very early on after the computer is turned on to protect against hackers at the early stage.
Mark