Yes, just edit over the name, title, etc of the old employee to the new employees info and save. Then have the new employee install it into their email program.
First check top of account page to see if you are already using the number of signatures that you have. If not, click the Add Signature button. If you are using the number of signatures available to your account and still need more, go to Account Information section of your account and click the upgrade button in the Subscription section in order to add additional signatures to your account. If you are using 1 of 1 signatures and can’t add any in the subscription section you may be using a corporate account in which case you are not allowed to add additional signatures to these accounts.
You will not be able to remove the first signature in your account although you can change the template to another one and set up a completely different signature by clicking the Customize button and then Change Design.