block1.jsx

class Press_ extends React.Component {
  render() {
    // React.cloneElement() requires a single child
    const Child = React.Children.only(this.props.children)

    // compute props to pass
    const propsToPass = {onPress: this.props.onPress}

    // return new element with props to pass
    // note: this could also be wrapped in other components, if we wanted
    return React.cloneElement(Child, propsToPass)
  }
}

class MyComponent extends React.Component {
  handlePress = () => {
    // ...
  }

  render() {
    return (
      <Press_ onPress={this.handlePress}>
        <div />
      </Press_>
    )
  }
}

ReactDom.Render(<MyComponent />, /* ... */)