How can we create a new tag in a Stack Exchange site?
A user with 1000 or more points has the Create Tags privilege. These user can create new tags simply by typing the name of the tag into the field where one adds the tags of a question, either when posting the question or via editing the question.
In case of doubt, it can be desirable to propose the tag in Tag management 2015 for some prior discussion.
This thread is also a way for newer users to propose a tag.
From Help Center > Privileges > Create Tags:
How do I create a new tag?
Simply enter a new tag with your question and it will be created. When creating your new tag, bear in mind that tags ...
- must be shorter than 25 characters
- must use the character set
You need at least 1k reputation points to be able to do this.
I will add that you should check carefully before creating a new tag whether there already is a suitable tag.
Before creating a new tag, check FAQ on tags for general advice on tagging, on creating new tags and on tag names used on this site.
It is also a good practice to create also tag-excerpt and tag-wiki for the tag, if you create a new tag. If you are below 20k your edit to the tag-info will need approval in suggested edits review queue. But do not let this fact scare you away. Tag-excerpts and tag-wikis are important for using the tag correctly. If you are creating a tag, probably you do this with the intention to help organize questions on this site better. Explaining the intended usage in the tag-excerpt might help this goal.