One option is Firefox Sync. However, that definitely is not 100% reliable, so you may want to also consider:

(A) Back up your currently active Firefox profile folder (and especially the logins.json and key4.db files)

See: Back up and restore information in Firefox profiles

(B) Export your saved logins to a CSV file

Note that this file is not secured in any way, so keep it in a safe location.

See: Export login data from Firefox and Import login and password data from a file

What is posted above is when you still have access to the old hard drive.

Do you mean that you already have a new hard drive, but didn't backup your personal data beforehand?

• https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles

In that case is it likely that you lost your saved passwords.