Just an example of Ansible playbook that runs docker-compose and then waits the MySQL container until it becomes ready. Tested on Ubuntu 18.04 LTS (Bionic Beaver).

playbook-docker-compose-moodle.yml

---
- hosts: moodle
  gather_facts: no
  become: yes

  tasks:
    - name: Install required packages
      apt:
        name: "{{item}}"
        update_cache: yes
      loop:
        - mysql-client
        - python3-pip
    - name: Update docker python package
      pip:
        name: docker
        state: latest
    - name: Install docker-compose python package
      pip:
        name: docker-compose
    - name: Set up the Docker services
      docker_service:
        project_name: moodle
        project_src: .
    - name: Get MySQL container IP address
      shell: docker inspect -f {% raw %}'{{ .NetworkSettings.Networks.moodle_default.IPAddress }}'{% endraw %} mysql
      register: mysql_ip
    - name: Wait until MySQL container is ready
      shell: mysql -u root -pmoodle -h {{mysql_ip.stdout}} -e 'show databases;'
      register: mysql_databases
      until: mysql_databases.stdout.find('moodle') != -1
      retries: 10
      delay: 2
      ignore_errors: yes