How long do the newly implanted hair follicles take to settle on the scalp?

Newly transplanted hair follicles should be secure within one week.  Many doctors have their own specific regimen after surgery.

Typically by 9 days following a procedure the grafts are well incorporated into the scalp and cannot be dislodged.

You may start to gym, heavy exercises and swimming 2 weeks after the FUE operation. Jogging, running, sauna, cycling etc don't give any harm after 2 weeks of operation . You can start to use minoxidil and other hair growth supportive drugs or food supplaments  (those contains biotin, zinc, folic acid, methionine, saw palmetto etc) 2 weeks after surgery. 

Newly planted grafts settle in the first day after the hair transplant and are usually stable. There is healing that is going on and many changes over the next month that will result in the new hairs that grow out