Giving Permission to Non-Admins to Manage the Taxonomy
Allow non-admins to create and edit filter groups and filters.
By default only system administrators can add and edit filter groups and filters. By changing this option, members of the provided user groups will be able to edit Targeted Search filters as well.
Navigate to the Targeted Search Configuration Page
Edit the 'Taxonomy User Groups' option
Click the pencil icon to edit the option.
Enter the name of a group
Enter as many groups as you want, separated by commas. Each group in this list will be able to access the Search Filters page to add and edit (and delete) filter groups and filters.