What is the equivalent for depends_on in kubernetes

I have a docker compose file with the following entries

version: '2.1'

services:
  mysql:
    container_name: mysql 
    image: mysql:latest 
    volumes:
      - ./mysqldata:/var/lib/mysql 
    environment: 
      MYSQL_ROOT_PASSWORD: 'password' 
    ports: 
      - '3306:3306' 
    healthcheck: 
        test: ["CMD", "curl", "-f", "http://localhost:3306"] 
        interval: 30s 
        timeout: 10s 
        retries: 5 

  test1: 
    container_name: test1 
    image: test1:latest 
    ports: 
      - '4884:4884' 
      - '8443' 
    depends_on: 
      mysql: 
        condition: service_healthy 
    links: 
     - mysql 

The Test-1 container is dependent on mysql and it needs to be up and running.

In docker this can be controlled using health check and depends_on attributes. The health check equivalent in kubernetes is readinessprobe which i have already created but how do we control the container startup in the pod's?????

Any directions on this is greatly appreciated.

My Kubernetes file:

apiVersion: apps/v1beta1 
kind: Deployment 
metadata: 
  name: deployment 
spec: 
  replicas: 1 
  template: 
    metadata: 
      labels: 
        app: deployment 

    spec: 
      containers: 
      - name: mysqldb 
        image: "dockerregistry:mysqldatabase" 
        imagePullPolicy: Always 
        ports: 
        - containerPort: 3306 
        readinessProbe: 
          tcpSocket: 
            port: 3306 
          initialDelaySeconds: 15 
          periodSeconds: 10 
      - name: test1 
        image: "dockerregistry::test1" 
        imagePullPolicy: Always 
        ports: 
        - containerPort: 3000 

This was purposefully left out. The reason being is that applications should be responsible for their connect/re-connect logic for connecting to service(s) such as a database. This is outside the scope of Kubernetes.