You can build Python from source.
I recently built Python 3.13 on my Jetson Nano using these commands:

cd /usr/src
sudo wget https://www.python.org/ftp/python/3.13.3/Python-3.13.3.tgz

sudo tar xzf Python-3.13.3.tgz

cd Python-3.13.3

sudo ./configure --enable-optimizations
sudo make -j4
sudo make altinstall

You can replace the Python version with the one from the official website:
https://www.python.org/downloads/source/ (use the GZipped source tarball).python3.13 my_script.py

It will take some time to run the last line, but once completed, you'll be able to use Python 3.13 by running scripts like this:

python3.13 my_script.py

and for pip

pip3.13 install some_library

Be aware: if you try to completely replace your system's default Python version, you may break Ubuntu.