Can I make an IRA contribution, under the new tax law, at any age?

Nothing has changed for the age when you can no longer contribute to a Traditional IRA.  The age remains at age 70 1/2 or younger.

For a Roth IRA anyone can contribute regardless of age.

DoninGA's answer applies to 2019; you are not permitted to make a traditional IRA contribution for 2019 if you were age 70½ or over in 2019.  The age restriction on traditional IRA contributions has been eliminated only for contributions made for 2020 and beyond.