I let my creative cloud license lapse for work. Now the apps don't work. I've purchased the license again through my job. When I install the apps, should I first trash the existing apps on my hard drive or will the installation use those existing apps on my hard drive and merely update them?
Since you have now purchased a Subscription again, you may simply Sign in to the Creative Cloud app or Individual Apps and they will give you the Option for Updating to the latest version and you may Update them. There is no need to Uninstall the existing Apps first and then re-install the Apps.