When we add a link to any answer or a user asks a question adding a link, our site should open a new page instead of launching the link on the same page.
The default behaviour of links is to open in the same page; this is true for all websites. Because this is the default, people expect links to open in the same page; as a developer, you can override it, but only if you have very good reasons to do so. (I don't see any in your question right now.)
If you do want to open a link in a new page/tab, you can rely on your browser's or operation system's capability to do so. On macOS, it's holding down Cmd when clicking; on Windows hold down Ctrl; other operation systems may be different. Right-clicking the link also works quite often.