No, it is not possible to transfer symbology from ArcGIS Online Map Viewer to ArcGIS Pro. There is currently no documentation on importing symbologies from ArcGIS Online to ArcGIS Pro.
However, it is possible to apply symbologies of a hosted feature layer from an ArcGIS Online web map to a local feature layer in ArcGIS Pro.
Ensure the data type of the hosted feature layer and the local feature layer are the same (polygon, polyline, point, or multipoint).
- Apply a style to a hosted feature layer in ArcGIS Online.
- Log in to ArcGIS Online.
- Click Content > My Content.
- Browse to hosted feature layer, click More Options , and click Open in Map Viewer.
- Apply a style to the layer. Refer to ArcGIS Online: Apply a style for further instructions.
- Save the web map. Refer to ArcGIS Online: Save maps (Map Viewer) for further instructions.
- Import the symbology of the hosted feature layer in ArcGIS Pro.
- Launch ArcGIS Pro, sign in to an ArcGIS Online organizational account, and create a new project.
- Add the web map created in Step 1 to ArcGIS Pro. Refer to ArcGIS Pro: Add a web map or web scene for further instructions.
- In the same map, add the local feature layer to apply the symbology to. Refer to ArcGIS Pro: Add layers to a map or scene for further instructions.
- Import the symbology from the hosted feature layer to the local feature layer. Refer to ArcGIS Pro: Import symbology to a feature layer for further instructions.
Save the symbol to a style to apply it to other feature layers in ArcGIS Pro. Refer to ArcGIS Pro: Save a point, line, or polygon symbol to a style for further instructions. Optionally, create a map package of the current map to save it on a local disk or share it in ArcGIS Online or ArcGIS Enterprise.
The image below shows the imported symbology is applied on the local feature layer, Libraries.