Starting with version 2.1, it is possible to add or open a tile package directly to a new map in ArcGIS Pro. For more information, refer to the following ArcGIS Help: What's new in ArcGIS Pro 2.1.
However, in previous releases of ArcGIS Pro (for example, version 1.4), a tile package cannot be opened directly, or be added to an ArcGIS Pro project either by using the Add Data button or by dragging the package from the folder and dropping it in the application. Tile packages can be used as inputs or outputs to ArcGIS Pro operations or geoprocessing tools. Hence, users must extract the tile package first using the Extract Package (Data Management) tool in ArcGIS Pro. The extracted package results in a raster or a layer file that can be opened and displayed in ArcGIS Pro.