You have six months according to state law to get a valid TN permit once you become resident of TN regardless of what other permits you have. Below is a quote from the applicable section of the TN law.
"If a person with a handgun permit from another state decides to become a resident of Tennessee, such person must obtain a Tennessee handgun permit within six (6) months of establishing residency in Tennessee. Such person will be processed as a renewal applicant if the eligibility requirements of the other state are substantially similar to the eligibility requirements of Tennessee. View application requirements by state for persons holding a Handgun Carry Permit from another state and applying for a Tennessee Handgun Carry Permit."
"Guns are for defending your life not for defending your pride."