Waiting for Subcription to finish in Angular

@Injectable(
  {
    providedIn: 'root'
  }
)
export class ExpenseHandlerService {

  //I think BehaviorSubject type should be Array<ExpenseDetails> instead of ExpenseDetails
  //As your question was not clear so I am assuming as Aray<ExpenseDetails>; If you want type as ExpenseDetails
  //then you will have to adjust the code accordinlgy
  //LETS KEEP THIS VARIABLE AS PRIVATE SO THAT NOONE FROM OUTSIDE CAN EMIT NEW VALUE
  //AND EXPOSE AN OBSERVABLE as public property [see below]
  private expenseDataChanged = new BehaviorSubject<Array<ExpenseDetails>>([]);

  //This should be subscribed by the consumers i.e. Components
  get expenseDataObs() {
     return this.expenseDataChanged.asObservable();
  }

  //NO NEED TO MAINTAIN THIS ARRAY AS BehaviorSubject.value will give us the last emitted array
  //private expenseData: Array<ExpenseDetails> = [];
  constructor( private http: HttpClient) {

    this.getExpenseData();

  }
/**
 * Fetched expense data and stored in the this.expenseData
 */
  getExpenseData() {
    console.log('Starting...');
    this.http.get("assets/model/data.json")
      .pipe(map(result => result)).subscribe(data => {

      //I AM NOT SURE IF YOU API CAN RETURN NULL OR NOT
      //STILL IF API RETURNS NULL THEN EMIT EMPTY ARRAY
      //ADJUST THIS CODE AS PER YOUR APP LOGIC
      if(!data) {
       data = [];
      }
      const arr = data as Array<ExpenseDetails>;

      //I AM NOT USING SLICE (with no argument will return same array) AS IT WAS NOT DOING ANYTHING;
      //IF YOU WANT TO USE THEN USE AS PER YOUR LOGIC
      this.expenseDataChanged.next(arr);
    });

  }

/**
 * Notifies other components of any change in the data
 *
 * @param data
 */
  addExpenseData(data: ExpenseDetails) {

    //Get the last emited array from behaviorsubject
    const lastEmittedArr = this.expenseDataChanged.value;

    //push the data in to newArray
    //NOTICE I AM CREATING NEW ARRAY - This is to make sure that array is rendered; again it is NOT mandatory
    //but it depends on kind of changedetection stretegy is used.
    const newArrayToEmit = [...lastEmittedArr, data];
    this.expenseDataChanged.next(newArrayToEmit);
  }
}

ngOnInit() {
    this.expenseHandlerService.expenseDataObs
        .pipe(

          //As soon as you subscribe the initial value could be an null because the Behavior subject was initialized with null
          //THIS IS BECAUSE OF THE NATURE OF BehaviorSubject; It may happen because by the time you subscribe
          //response of HTTP API might not have recieved; but as soon as it is received
          //Using the filter will ensure to avoid null in callback
          filter(arr => !!arr)
        )
        .subscribe((res) => {

      //Process the array recieved;
      this.receiveExpenseData(res);
    });
  }