Although people were still writing and painting pictures about falconry (which primarily used hawks), it had just about died out as a pastime during the Regency because of the prevalence of guns in hunting (guns don’t have to be fed and trained, I suppose). By our period there was supposedly only one falconer left in all of England. But falconry was taken up by those crass Americans, and it was also still common in certain countries on the Continent. The English just preferred their rifles.