Remove google-account from older smartphone I gave my sister my older smartphone without removing my google-account.

How can I remove that permission without removing her settings completely, or how can I remove that certain android device from my google dashboard?

If possible, it would be great if I could do it remotely (via my google dashboard).
If you are using Google Two Step authorisation, then you can revoke the one-time password that you assigned to the phone remotely from your Google account's settings, I don't think that this is possible unless you are using the Two Step authorisation.

Go to your Google Account Settings page, click the Edit link beside "2 step verification", click "Manage application-specific passwords", look down the list for the password assigned to your old phone and click the "Revoke" link. Next time the phone tries to access your Google account, it should be denied access and your sister will see a warning asking her to enter the new password.

If you haven't set up the two step authorisation then, to do it directly on the phone, as long as the phone is running Android 2.1 (Eclair) or newer, then you can go into Settings -> Accounts and sync -> then select the account and you should have a Remove account button at the bottom of the screen.

Once you've done this switch the phone off and on again (just to make sure that no apps are running that have already logged in), and it should be removed.

Note that this won't remove all of your old data from the phone, it will just remove some of the Google synced data, and stop anything new from coming down from (or going up to) your Google account. To be sure that all of your old data is removed from the phone, you will need to wipe the phone with a factory reset.