Yes, it is possible to use tax in a previous tax year to cover Gift Aid
If you donated in 2019/20 but didn't pay enough tax that year to cover Gift Aid, you can ask HMRC for the tax you paid in 2018/19 to cover it. This would usually be done after the end of the tax year in which you made the donations (so the total amount needed is known).
You can do this by sending a simple email/letter to HMRC with the following:
"Of the donations I made in the last tax year, I would like "x" pounds to be applied to the previous tax year"