Redgate licensing is user based (with the exception SQL Backup, SQL Monitor and SmartAssembly) so when activating licenses, if you are logging in with the same Redgate ID each time then you will be able to activate on as many machines as you need without running out of entitlements.
If you are getting the activation error 'Failed to activate the license: All of the entitlements for serial xxx-xxx-xxxxxx-xxxx have already been claimed' you may not be logged in. On the toolbar click on Help > Manage license and you'll see if you're logged in.
If you're not logging in with your Redgate, you have changed your email address or other people are using the license, you may get a message saying there aren't enough entitlements left on the license. If this happens you will need to log in to the customer portal and remove an old activation:
You will need to contact the license owner/admin if you can't see the license in your account.
NOTE: User based licensing does not support tool versions prior to 2017 so if you're activating an old license the activation will show in the customer portal as Not logged in.