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In case that

  1. I have understood your (very brief) question and
  2. you’re not actually talking about the post_tag-taxonomy

then you have wp_insert_term(), which is the underlying API function.

Edit

As to the comment, there’s the need of meta data for a term and administrator approval.

WordPress currently has no native way of adding meta data to a taxonomy taxon. There’re ideas “around” it. IMHO they clutter your DB-options table in seconds without a reason. There’re other ways around this, but this would be too much for a single answer, so I can only recommend to find another way of handling tag maintenance.