All employees, regardless of participation in an employer-sponsored retirement savings programs such as the TSP and regardless of income, are eligible to contribute to some type of IRA. The type of IRA you can contribute to will depend on: (1) whether you are covered by a pension plan and/or qualified retirement plan; (2) your modified adjusted gross income (MAGI); (3) your age; and (4) the amount of your, or your spouse’s if married, earned income.
Many federal employees are not eligible to make a traditional deductible IRA contribution because they are covered by a qualified pension plan – CSRS or FERS -- and their MAGI is above the threshold; however, in that case, they are eligible to make a traditional nondeductible IRA contribution (up to age 70.5). And they can make a Roth IRA contribution no matter their age so long as their MAGI does not exceed the higher limits applying to that type of IRA.
The MAGI levels for determining deductibility typically increase each year due to inflation adjustments and sometimes increase due to a change in law; current levels are at www.irs.gov/Retirement-Plans/IRA-Deduction-Limits.