One might ask "How can you have mixed franking on mail when there is only one post office?". The answer is create a new country and post your letter while the stamps of both the new and old regimes are available and legitimate!
The cover shown here is from Dublin to Berlin on 11 April 1923. The Free State 2d stamp was issued on 12 June 1922, and the 1d on 23 February 1923. The three line overprint was issued 18 December 1922. The time of validity for the use of the overprinted British stamps was coming to an end as more of the Irish definitives came into service.
The appropriate rate was 3d. The amount on cover is 3½d - overpaid by ½d. The cancel is a Dublin "Learn Irish" slogan cancel.