The first step with creating a front end form to allow users to edit a term would be supplying the correct post ID when calling acf_form().
For an existing term the post ID you need will be "term_{$term_id}"
For allowing them to create a new term you would need to build a pre_save_post filter that creates the term and sets the correct post ID to be returned to ACF so that it can to the updating https://www.advancedcustomfields.com/resources/acf-pre_save_post/. In this case you would use something like "new_{$taxonomy)_term" for the post ID and use this in your conditional at the beginning of your filter.
