Unlike some other email programs, Thunderbird does not create a clickable link when you are composing a message and add a hyperlink. If you use the Insert > Link... command, the link is formatted as a link (underlined and colored), but if you click it nothing happens. If you paste or type a link into the body of a message it appears in the text of the message without any indication that it is a link.
This behavior is deliberate. When links are "activated", they are difficult to edit (because when you try to position the cursor within an active link you usually launch the link in the browser).
When a message is sent (or saved as a draft), Thunderbird "activates" links in the message, adding formatting as necessary and making them clickable hyperlinks.
When you click a hyperlink in a message, your system's default web browser should open (if it is not already running) and display the link. If that doesn't happen, there are several possible causes.
Every operating system allows the specification of a default browser that will be launched (for example) when a hyperlink in a message is clicked. Internet Explorer, Firefox, and other browsers check this setting by default when they start up and prompt you to set them as the default. Sometimes, however, this setting goes awry and your computer forgets which browser is the default. To fix this problem, you need to reset the default browser on your system.
See Make Firefox your default browser for instructions. Then restart Thunderbird.
See Microsoft's article Make Internet Explorer your default browser for instructions. Then restart Thunderbird.
See Microsoft's article Make Microsoft Edge your default browser. Then restart Thunderbird.
In Thunderbird, you can specify an action that occurs when you click on various types of attachments and inline content. If the action for the HTTP / HTTPS content type is set incorrectly, this will prevent links from opening correctly.
If the operating system's default browser is specified correctly as described above, it is not necessary to specify an action for the HTTP / HTTPS content type. To check this setting, select Tools > OptionsEdit > PreferencesThunderbird > Preferences and click on the Attachments panel. If HTTP and/or HTTPS are listed in the Content Type column, either delete the action or ensure the specified action is correct.
In some circumstances, a normally hidden preference gets changed, resulting in Thunderbird trying to handle these links internally. One of these circumstances appears to be after you uninstall the ThunderBrowse add-on, although the upgrade process to V5 appears to have caused it for some people as well. To check if this might be the cause, open the Troubleshooting Information in the Help menu and under the Important Modified Preferences heading, look for a preference called network.protocol-handler.external-default or any other preference beginning with network.protocol-handler.warn-external. If any of these are present and set to false, then this is your problem.
To correct this setting, use the Config Editor to change the hidden preferences from false to true. Type network.protocol-handler.external-default into the field, or at least so much of it that the entry appears in the list below. Select the entry in the list, right-click it and select the Reset option from the menu that appears.
It is time to look for an extension that may be causing some unwanted behavior. Run Thunderbird in Thunderbird Safe Mode. If you can click on hyperlinks in Thunderbird Safe Mode but not in normal mode, your problem is probably being caused by an add-on (also known as an extension).
Next, try the Standard Diagnostics.
If you still have a problem, go here and ask about what could be the cause. Before you post your question, be sure to say exactly what you have done already to diagnose the problem.