You can intersect the whole or a selection of the elements of two layers:
Select the Intersection function from Tools -> Geoprocessing in the menu bar.
From the drop-down menus, select the layers whose elements will be intersected.
Press Execute. To intersect the selected elements, check the relevant box. The resulting elements of the intersection appear colored and are added to the Annotations layer. These are new geometries resulting from the individual intersection of each of the geometries of the first layer with each of the geometries of the second layer.
You can then copy them to another layer displayed in the application if you have permissions to add elements to it.