A transfer within the same state system, from Bledsoe County Correctional Complex to Northwest Correctional Complex, both Tennessee Department of Correction facilities, is significantly smoother than an interstate or county-to-state transfer in terms of how quickly privileges carry over.
Because both facilities operate under the same TDOC system, your boyfriend's existing approvals, account information, and general status transfer with him rather than requiring the full orientation and intake process that a new system entry would trigger. Phone access in this situation should come back online very quickly, often within a day or two of arrival and processing at NWCX.
The one exception is if he arrives at NWCX in a segregated housing status. If the transfer was disciplinary or if he is being housed in restricted status at the new facility for any reason, phone privileges would be subject to the SHU restrictions that apply to segregated inmates. In that case the timeline extends significantly until the segregation status is resolved.
Assuming he is going into general population at Northwest Correctional, expect phone access to restore within a few days at most. Make sure your number is confirmed in his approved contact list, which should have transferred with his file, and that there are funds on his phone account so nothing delays the first call on his end.
A letter sent to NWCX now through InmateAid ensures something is waiting for him as he gets settled at the new facility, which is always a welcome arrival during any transition.