Styling not applying to child component

It's because by default components have view encapsulation (shadow dom). To disable this behavior, you can leverage the encapsulation attribute, as described below:

import {Component, ViewEncapsulation} from '@angular/core';
import {TestApp} from 'testapp.component.ts';
@Component({
  selector:'test-component',
  styleUrls: ['test.component.css'],
  templateUrl: './test.component.html',
  directives:[TestApp],
  encapsulation: ViewEncapsulation.None // <------
})
export class TestComponent{

}

See this plunkr: http://plnkr.co/edit/qkhkfxPjgKus4WM9j9qg?p=preview.

When using the styleUrls property, the styles are local to the one component, not to its children. So I made two changes: 1) Moved the styleUrls to the testapp component. 2) Moved the div to the testapp component.

import {Component} from '@angular/core';
@Component({
 selector:'testapp',
 styleUrls: ['./test.component.css'],
 template: `
 <div class="test">
  <a href="https://www.google.com">Google</a>
 </div>

 `

})
export class TestApp{

}