Statute 014 "CHANGE OF NAME OR ADDRESS OF PERMIT HOLDER".Subsection 014.01 notes that permit holders who do this are required to notify the NSP in writing within 30 days of the change.
Subsection 014.02 notes that the permit holder may obtain a replacement permit by.... ...
the NSP shall issue a replacement permit within 5 working days of receiving the request.
I was personally involved with such address change this past summer and followed the statute and subsections. The information process is on the NSP website
https://statepatrol.nebraska.gov/services/concealed-handgun-permits/how-apply/renew/update-name-address. Their site also allows you to do the address change online with their link
https://www.nebraska.gov/apps-nsp-chp/, which I did and printed off the receipt to keep with me while I was waiting for the replacement CHP within the expected 5 working days of having submitted the requested information.
By week 3 of
not having received the renewal permit, I called NSP who politely informed me that they were behind because they were processing about 2,200 CHP applications at the time. They also told me that I was covered by the receipt should I be officially stopped by LEO while I had a discrepancy of addresses between my new driver's license and my current CHP.
I received the renewal permit during week 6 from the initial online submission.
Hope this helps.