[example]$ cat docker-compose.yml 
services:
  frontend:
    image: nginx
    ports:
      - 8888:80
    depends_on:
      backend:
        condition: service_completed_successfully
  backend:
    image: busybox
    command: sh -c 'sleep 10'

[example]$ docker-compose up -d
Creating network "example_default" with the default driver
Creating example_backend_1 ... done
Creating example_frontend_1 ... done

[example]$ docker ps -a
CONTAINER ID   IMAGE     COMMAND                  CREATED          STATUS                     PORTS                  NAMES
fc81eefac293   nginx     "/docker-entrypoint.…"   4 seconds ago    Up 3 seconds               0.0.0.0:8888->80/tcp   example_frontend_1
1278dc861a94   busybox   "sh -c 'sleep 10'"       15 seconds ago   Exited (0) 4 seconds ago                          example_backend_1

[example]$ docker compose up -d
[+] Running 3/3
 ⠿ Network "example_default"     Created                                                                                 0.0s
 ⠿ Container example_backend_1   Started                                                                                 0.3s
 ⠿ Container example_frontend_1  Started                                                                                10.9s

[example]$ docker ps -a
CONTAINER ID   IMAGE     COMMAND                  CREATED          STATUS                     PORTS                  NAMES
c825111982dd   nginx     "/docker-entrypoint.…"   14 seconds ago   Up 2 seconds               0.0.0.0:8888->80/tcp   example_frontend_1
1babc6992a3b   busybox   "sh -c 'sleep 10'"       14 seconds ago   Exited (0) 3 seconds ago                          example_backend_1