Add a context menu and a click event on a button/span/div/etc that references the local variable (cm in this example) and calls the show or toggle function.

<p-contextMenu #cm [model]="items"></p-contextMenu>

<button (click)="cm.show($event);$event.stopPropagation();">Show context</button>

Feel free to pass this to a function which will handle it:

(click)="showContext(cm, $event)"

In the TS:

showContext(cm: ContextMenu, event :MouseEvent) {
  cm.show(event);
  event.stopPropagation();
}

The most important thing that seems to be necessary (at least on PrimeNG 7) is the event.stopPropagation(). Without it, if you view the DOM, you will see the context menu reacting to the show() event but the display stays as none.

The other important thing is passing the mouse event in the show() which lets the context menu appear where your cursor is, otherwise it appears elsewhere on the page.

If attempting to call the show/toggle purely through code and using the ViewChild without a click event happening, you can try to manually edit the style and change the display:none to a display:block (as detailed in the comment by Y. Tarion)

You can open programmatically a contextMenu PrimeNG but it's a little tricky.

Your ContextMenu in your template :

<p-contextMenu #cm [global]="true" [model]="items"></p-contextMenu>

On your button : (click)="toggle($event)"

On your typescript, here an example of the toggle method :

  toggle(event){
    if(!this.cm.containerViewChild.nativeElement.style.display ||
      this.cm.containerViewChild.nativeElement.style.display == 'none') {
      //Open contextual menu
      setTimeout(() => {
        this.cm.position(event);
        this.cm.containerViewChild.nativeElement.style.display = 'block';
        this.cm.containerViewChild.nativeElement.style.visiblility = 'visible';
      }, 0);
    }else{
      //close contextual menu
      setTimeout(() => {
        this.cm.containerViewChild.nativeElement.style.display = 'none';
      }, 0);
    }
  }

Where cm is your ContextMenu

@ViewChild("cm") cm:ContextMenu;

Or, it exists an alternative from the ContextMenu for this use case : the PrimeNG's tiered menu