The sort dropdown from the GD > Loop Actions block shows on category and post type pages, but GeoDirectory hides it on search results. Search results are put in order by the search itself:

• If the search has a location (typed in the Near field, or the visitor’s own location), the nearest listings come first.
• If there is no location but there are keywords, the best matches come first. Listings with the words in the title rank above listings that only mention them in the description.
• Otherwise the post type’s default sort order is used. You set that at Places > Settings > Sorting.

Let visitors narrow down search results

If visitors need to filter results by a feature, for example vegan or not, price range or opening hours, use the Advanced Search Filters add-on. Each custom field you choose becomes a filter in the search bar or in the filters panel, and the filters are applied to the search results.

See How to add a filter to the advanced search filters and How to filter listings by “Open Now”. For more on how keywords and locations are matched, see How does the GeoDirectory search work.