How tp restart interval?

If you use timer instead of interval, and set the initial delay to 0, then your interval will fire immediately.

You can use takeUntil operator to prevent the interval to run always, and repeatWhen operator to restart it whenever you want:

import { Observable, Subject, timer } from 'rxjs';
import { repeatWhen, switchMap, takeUntil } from 'rxjs/operators';

export class RepeatingServiceCall<T> {
  readonly observable$: Observable<T>;
  private readonly _stop = new Subject<void>();
  private readonly _start = new Subject<void>();

  constructor(serviceCall: () => Observable<T>, delay: number) {
    this.observable$ = timer(0, delay)
      .pipe(
        switchMap(() => serviceCall()),
        takeUntil(this._stop),
        repeatWhen(() => this._start)
      );
  }
  start(): void {
    this._start.next();
  }
  stop(): void {
    this._stop.next();
  }
}

Here is a working StackBlitz example.

P.S.: Getters and setters are working different in typescript. So you do not need classic getter concept, you can just make the attribute public and readonly.