Just to document an alternative solution, which I had to come up with because I found that the Geometry Paster plugin had some limitations with geometries that had large numbers of vertices.
There are also some different situations which required a bit more flexibility, or less map interaction, which the solution below allowed me to have.
I use the Field Calculator on a single record selection.
Select the 'Update Existing Field' and under there, there is '' available as an option.
Then - it depends on where the source of the geometry is coming from, but lets say, the source is from another layer which has a record that contains the geometry I want in the destination layer.
The following expression will work.
geometry(get_feature_by_id(layer,feature_id))
Where 'layer' is simply the name of the layer as derived from the Map Layers listing. eg: 'permit_5ce54d18_5c0b_4297_930f_2212956c9e78'
feature_id is just the fid, or other record ID.