Leanna there's not really any built-in solution.
If the "other" tag is a new tag or if there are very few discussions in the new tag, then consider renaming the existing one, then manually change the tags of the few discussions that needed to stay in the deleted-and-recreated tag. It will be the easiest.
If you need to move many existing discussions into another existing tag with many discussions as well, you can use an SQL query in the database. Update the tag_id of the discussion_tag table, eventually taking into account duplicate keys if there's a possibility of one of the discussions having both the new and old tag already. backup before attempting
Last solution that's probably not quickly nor cheap would be to get a mass-tag-manager extension commissioned.
