I think you can close out the session and re open it again for another 15 minutes. Even so that can be an inconvenience though.  As 15 minutes can go by pretty quick sometimes.
 
I think the 15 minute thing does allow you to demo some third party software and then after you pay the money it will work for unlimited time but still in the player. 
 
I am not an expert on this either but I think also that if a third party instruments needs the full version of Kontakt you may have to have that to even demo it.  There would obviously be some sort of other restriction imposed.
 
I don't have the full version of Kontakt, only the player.  I know that there are some instruments that will work in the player but for only 15 minutes at a time as well even for fully paid versions but will be normal in the full version of Kontakt.  I tend to avoid those.
 
Maybe some full Kontakt owners can chime in. They will know more about what the full version does, demo and paid.

Jeff Evans
I think you can close out the session and re open it again for another 15 minutes. Even so that can be an inconvenience though.  As 15 minutes can go by pretty quick sometimes.
 
I think the 15 minute thing does allow you to demo some third party software and then after you pay the money it will work for unlimited time but still in the player. 
 
I am not an expert on this either but I think also that if a third party instruments needs the full version of Kontakt you may have to have that to even demo it.  There would obviously be some sort of other restriction imposed.
 
I don't have the full version of Kontakt, only the player.  I know that there are some instruments that will work in the player but for only 15 minutes at a time as well even for fully paid versions but will be normal in the full version of Kontakt.  I tend to avoid those.
 
Maybe some full Kontakt owners can chime in. They will know more about what the full version does, demo and paid.

Thank you, Jeff!
fj

There are lots of cheap libs out there for Kontact (gd spellcheck). Most need the full version, which is on sale summer and Christmas. If you are looking for free libraries, look elsewhere unless you get the paid version. NI wants lib makers to pay them.

The best free libs and player is soundfonts.