How qualification works in New Mexico
New Mexico has a real trap worth flagging carefully: its own retired-officer concealed-handgun license (N.M. Stat. § 29-19-14, N.M. Admin. Code 10.8.2.31) is a separate, New-Mexico-only 5-year permit with its own cadence (no annual retest required until an officer has been retired more than 10 years) -- it is NOT a LEOSA-compliant annual qualification, and someone relying on it alone could not lawfully rely on it for nationwide LEOSA carry. Separately, the New Mexico Department of Public Safety runs its own internal annual LEOSA qualification program (the authorized DPS off-duty course of fire, issuing a "Retiree LEOSA Certification Card"), but — like New York's and Connecticut's state-trooper-only programs — that program is for retired DPS commissioned employees specifically, not a universal standard for every New Mexico agency's retirees.
What to carry afterward
Where LEOSA doesn't apply
Not legal advice. Confirm with New Mexico's POST commission or your former agency.