It could be immediate if the inmate is transferring within the same system like state or federal prison. If they are going from county to state or federal it could take up to 30 days before they are permitted visits or phone calls. That is on the long side, sometimes the delay is as little as seven days.
https://www.inmateaid.com/ask-the-inmate/after-being-transferred-how-long-does-it-take-to-process-the-inmate-in-before-he#answer
Accepted Answer Date Created: April 29,2016