I accidentally created new tag while editing a question. I need to remove from this site. Is there any privileges required to do so? Or It will automatically get removed after I delete from the question (because that was only tag which is now removed)?
Yes, tags get automatically removed if there are no questions tagged with them. That's the only way normal users can remove a tag.
I wouldn't worry about it, just wait a while and it will disappear. Unused tags are purged automatically once a day.