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
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**