Once your freshly caught Red-tailed Hawk tires of bating off the fist and sits quietly, your next goal should be to . . .

The most appropriate next step when your freshly caught Red-tailed Hawk settles quietly after bating off the fist is to get it to feed off the fist. This step is crucial for building trust and establishing a positive bond between you and the hawk. Feeding directly from the fist encourages the bird to associate you with food and security, which is fundamental in the initial training stages.

This action also helps the hawk to calm down and focus on you, rather than on its environment. Feeding off the fist reinforces the idea that you are the source of sustenance, which is essential for its acclimatization to captivity and your role as a falconer. By successfully achieving this step, you can facilitate a smoother transition to future training phases.

The other options, while relevant in the training process, don’t align with the immediate goal after the hawk has calmed down. Introducing it to wild game would be premature at this stage, as it hasn't yet established a connection with you. Lure flying can come after trust is built through feeding, as it requires a deeper level of engagement and understanding between you and the bird. Tying the hawk to a block perch might restrict its mobility and would not build the necessary bond at this critical moment.