After installing browser extension 1Password 7 should work without restarting 1Password.
If that is not technically possible, then should communicate restart of 1Password is required. This restart includes restarting the status menu bar 1Password app, ie "Quit 1Password Completely" is necessary.
Env: MacBook Pro / macOS 10.14.1 (18B75) "Mojave" / 1Password 7 Version 7.2.2 (70202006) AgileBits Store /
Firefox 63.0.3 (64-bit) / Firefox 1Password extension 188.8.131.52
This is a "new user" / "first run" scenario. I experienced this symptom while setting up this new MacBook Pro. All described applications are newly installed and up-to-date.
I experienced this symptom in Safari and Chrome. I rebooted the computer to try to resolve after I thought I had completely quitted 1Password and thought that did not appear to resolve it. Rebooting resolved the symptom. After investigating the issue further, I now doubt I successfully completely quit 1Password prior to going the reboot path. As 1Password has a macOS menu bar component rebooting the computer would likely be the way most people workaround this issue.
I don't know if in Safari or Chrome, the 1Password extension icon was greyed out. I think like most people I don't have much exposure with disabled / non-functioning extensions. I was focusing on why 1Password kept prompting me to install the extension again.
After installing the Firefox browser extension for 1Password , the extension does not work until after 1Password has been quit.
Consider the excellent step-by-steps at https://1password.com/browsers/firefox/ which includes the following (annotated by me):
The action behavior is that the extension does not successfully enable. Worse then no communication of the experienced behavior, you are prompted to install the extension yet again:
"Quit 1Password Completely" accessed from macOS menu bar 1Password resolved this.
Hope this helps.
1Password Version: 7.2.2 (70202006)
Extension Version: 184.108.40.206
OS Version: 10.14.1 (18B75)
Sync Type: Not Provided
Referrer: forum-search:1Password 7 restart required to use browser extension after installing