Once you have money in an HSA, you can withdraw it for medical expenses at any time without penalty, even if you change insurance plans.
If you change insurance plans in the middle of the year, you become ineligible to contribute to an HSA as soon as you are covered by a non-eligible insurance plan. Your annual contribution limit is prorated on a monthly basis, determining your insurance status on the first day of each month.
If you have already contributed more to the HSA than your adjusted contribution limit with the new job, you have to withdraw the excess. Contact the HSA bank and ask for a withdrawal of excess contribution. This is a different procedure than a regular withdrawal. The bank must also return any earnings attributed to the excess contribution, and that will be included in your taxable income.
If you have not contributed the new maximum amount, you can continue to make contributions to the HSA even after you change jobs. Your contribution limit is determined by the type of insurance coverage you have, but the exact timing of the contributions does not matter, as long as they are made before the end of the tax year. (For example, if you start your new job September 1, and you had a single HDHP, your maximum HSA contribution for 2022 will be $2433. If you had only contributed $1800 so far, you could contribute an additional $633 even after September 1, as long as your annual contribution total does not exceed your annual contribution limit.)
