In order to migrate to the latest Python release before the Anaconda Download packages haven been upgraded to it (in my case Python 3.8), I had to first upgrade my Conda installation:
conda update -n base -c defaults conda
And then create a new Python 3.8 environment:
conda create -n py38 python=3.8
Unfortunately, a couple of packages are not yet there, so installing the full Anaconda package does not work. So the solution was to update conda and install packages manually:
conda install ipython conda install numpy conda install scipy conda install matplotlib conda install pandas conda install jupyter conda install astropy conda install scikit-learn conda install seaborn conda install pillow
And now I can (hopefully) use the improved performance of Python 3.8 (benchmarks coming soon).
Packages not available through Conda still have to be added through PIP:
pip install --upgrade photutils pip install --upgrade montage-wrapper pip install --upgrade emcee pip install --upgrade pymc pip install --upgrade glueviz pip install --upgrade aplpy pip install --upgrade fits_tools pip install --upgrade healpy pip install --upgrade uncertainties pip install --upgrade pysqlite2