1. Install all the system-level dependencies:

apt install mercurial python3-dev python3-numpy libav-tools 
apt install libsdl-image1.2-dev libsdl-mixer1.2-dev libsdl-ttf2.0-dev 
apt install libsmpeg-dev libsdl1.2-dev  libportmidi-dev libswscale-dev libavformat-dev libavcodec-dev

2. Install pip package in system default Python3:

python3 -m pip install -U pygame --user

or install in virtual environment:

source your_venv_path/bin/activate
pip install pygame

PyGame is looking for these packages:

Hunting dependencies…
SDL : found 1.2.15
FONT : not found
IMAGE : not found
MIXER : not found
PNG : found
JPEG : not found
SCRAP : found
PORTMIDI: not found
PORTTIME: not found
FREETYPE: found 2.6.3
Missing dependencies