At first I was not sure but then reading Live Server believe you are looking for auto-refresh feature using VS Code Live Server extension.
Following article covers the details of it:
VS Code Live Server – How to Auto-Refresh Your Browser with this Simple Extension[
^]
For issues around getting it up, have a look at:
Visual Studio Code Live Server Not Working[
^]. As explained there, you might need to try these:
1. Restart VS Code
2. Set the browser for Live Server
3. Set the default browser for your operating system
4. Go to the live page yourself
Make sure LiveServer is running - as long as it is, you should see your page.