If you'd like the email to automatically apply a signature, review your signature settings again.

To get to your signature settings in Classic Outlook, you will select "File" in the top left corner, then "Options". In the popup, there will be an option that reads "Mail." When you select "Mail", you will have to look for the option in the screenshot provided below. Once you find it, select "Signatures..." 



In Webpage Outlook, you will choose "Insert", then select the "Signature" dropdown arrow. You may see a list of your saved signatures, and "Signatures..." at the bottom of the list. Select "Signatures..." 




You should now be in the Signatures and Stationery / Email Signature menu. I will be providing both classic outlook and webpage outlook screenshots.





You'll notice where it says, "New Messages" and "Replies/Forwards" there's a small note that says "(none)" and a dropdown arrow. 

When you have the signature you want to use ready to go, click on the dropdown arrow and choose the signature name. Then, select OK or Save in the bottom right corner.
For example, if I want to use "LTC Signature" instead of "Silly Signature", I'd choose "LTC Signature" in the dropdown menu beside New Messages. Then, select Okay / Save. This will set up your email account so that when you compose a new message, the signature should already be inside of the email. 
When you choose the signature you want in the "Replies/Forwards" dropdown menu, this will set up your email account so that when you reply to, or forward a message to another recipient, it will automatically apply your signature in the message. Remember to select Okay / Save to save the settings you've chosen. 



In the screenshots below, I have chosen "New Email / Compose". The signature automatically populates in the body of the email since I have selected the email in "New Messages". The signature will also automatically populate when you reply to emails, or forward emails if you chose this option.