It’s not built-in to auto-close HTML tags, but you can use the Text Snippets plugin.
I have, for instance, these text snippets defined:
kbd : <kbd>$end$</kbd>
sup : <sup>$end$</sup>
sub : <sub>$end$</sub>
This allows me to type sub, press the defined expansion key, and voilà, it will insert <sub>|</sub> and place the cursor where I put the | here.