I found out that I can press 'a' or 'd' to navigate to next or previous posts.
Though, it navigates to the post that was uploaded before or after current post even when I entered that post through tag search.

Is there a way to navigate to next post but only within the tag search results?

If you have a search result, the a/d navigation will prioritize that. You can also use this to navigate through pools.

It should work this way by default. Make sure you don't have the "Enable post navigation" option disabled in your account settings.