My wife worked for a school system in Texas (TRS) and has retired. She paid very little into Social Security in her life - mostly as part time work and never reached 40 credits. She was previously married for 35 years. It appears she is not eligible for spousal benefits on her previous husband. Is she eligible for a portion of mine? We have been married for 3 1/2 years. I am 70 and have been receiving benefits since 62. She is now 65.
Your wife can likely qualify for Medicare coverage based on your record, but if she's already receiving her teacher's pension, the Government Pension Offset (GPO) provision would likely eliminate or greatly reduce her potential spousal benefits from your record (https://www.ssa.gov/pubs/EN-05-10007.pdf). Essentially, her spousal benefits would be reduced by 2/3rds of the amount of her teacher's pension, which could well reduce the rate to zero. It wouldn't hurt for her to check with Social Security to be sure, though.