What if was covered by an employer retirement plan for only part of a year. Can I qualify for a tradional IRA?

You are covered by a retirement plan all year if only covered for one day.  You can always contribute to a Traditional IRA if you have earned income.  The limit is the amount that is deductible.

See this IRS link for IRA deduction limits when covered by a retirement plan at work.

https://www.irs.gov/Retirement-Plans/IRA-Deduction-Limits