You will likely have to get in touch with your VAR or SolidWorks Corp and explain what happened. They will be able to get it switched from a trial to full.
As long as you still have a serial number, you can reactivate the license
I think Christian Chu is correct. I believe as long as it is on the same computer, it should be recognized as the same system and should install without issues.
I am assuming that you are saying that your subscription is active until June 2018, which means that your VAR should help you if you have any issues activating.
If your installation is a stand-alone you will need to contact your VAR so that they can free your serial number.
If your installation is server-side, no worries the licencing is managed by the server's licence manager.