I made a version that uses character length rather than div size.

import { Component, Input, ElementRef, OnChanges} from '@angular/core';

@Component({    
    selector: 'read-more',
    template: `
        <div [innerHTML]="currentText">
        </div>
            <a [class.hidden]="hideToggle" (click)="toggleView()">Read {{isCollapsed? 'more':'less'}}</a>
    `
})

export class ReadMoreComponent implements OnChanges {
    @Input() text: string;
    @Input() maxLength: number = 100;
    currentText: string;
    hideToggle: boolean = true;

    public isCollapsed: boolean = true;

    constructor(private elementRef: ElementRef) {

    }
    toggleView() {
        this.isCollapsed = !this.isCollapsed;
        this.determineView();
    }
    determineView() {
        if (!this.text || this.text.length <= this.maxLength) {
            this.currentText = this.text;
            this.isCollapsed = false;
            this.hideToggle = true;
            return;
        }
        this.hideToggle = false;
        if (this.isCollapsed == true) {
            this.currentText = this.text.substring(0, this.maxLength) + "...";
        } else if(this.isCollapsed == false)  {
            this.currentText = this.text;
        }

    }
    ngOnChanges() {
        this.determineView();       
    }
}

Usage:

<read-more [text]="text" [maxLength]="100"></read-more>

I think you'll need a Component rather then Directive. Components makes more sense since you need to add Read more button/link, i.e. update DOM.

@Component({
    selector: 'read-more',
    template: `
        <div [class.collapsed]="isCollapsed">
            <ng-content></ng-content>
        </div>
        <div (click)="isCollapsed = !isCollapsed">Read more</div>
    `,
    styles: [`
        div.collapsed {
            height: 250px;
            overflow: hidden;
        }
    `]
})

export class ReadMoreComponent {
    isCollapsed = true;
}

Usage:

<read-more>
   <!-- you HTML goes here -->
</read-more>