Appliance restarting when I activate the license

Can you grep the ltm logs and share it. I doubt re-license has anything to do with the reboot. Did you do via GUI or CLI.

Well i've seen this happen often in my lab too... Configuration utility becomes unresponsive. I go into the CLI and restart the tomcat service and it starts working.

bigstart restart tomcat

Also you could check the logs in /var/log/tomcat/catalina.out

Still, you can do the re-activation through CLI itself...

tmsh show /sys hardware | grep ‘Registration Key’
grep -i "Registration Key" /config/bigip.license
cp /config/bigip.license /config/bigip.license.backup
get-dossier –b <Registration Key>
reloadlic

Refer these SOL if you need -

https://support.f5.com/kb/en-us/solutions/public/2000/500/sol2595.html

https://support.f5.com/kb/en-us/solutions/public/14000/500/sol14528.html