HSA Contributions without relation to employment

Yes, you generally can contribute to an HSA that you had set up while you were with a former employer. However, you are only able to contribute to any HSA if you are an HSA-eligible individual. According to IRS Publication 969:

Qualifying for an HSA

To be an eligible individual and qualify for an HSA, you must meet the following requirements.

• You are covered under a high deductible health plan (HDHP), described later, on the first day of the month.
• You have no other health coverage except what is permitted under Other health coverage, later.
• You aren’t enrolled in Medicare.
• You can’t be claimed as a dependent on someone else’s 2019 tax return.

If you meet these requirements, you can contribute to an HSA. If you aren't sure whether or not your health plan qualifies as an HSA-eligible HDHP, ask the health insurance company. There are stiff penalties for contributing to an HSA when you are not eligible, and there are annual limits to the HSA contributions.