The postcard above shows the Royal Hotel's driveway and entrance and below is a second picture of the building taken from a slightly different position. The older part of the hotel, designed in the Gothic style, was at the front of the building. The newer wing at the rear, opened in 1908^[1], was architecturally quite different. It was the only part of the structure to survive the disastrous fire of Easter Monday 1929. Mr. Bray, who was the proprietor in 1929, had "spent thousands of pounds in the previous months renovating the hotel^[2]". With the roof gone and so much water damage the main building had to be demolished.

The surviving wing of the hotel can be seen on a couple of other postcards on this web site; the foundations of the Royal Hotel are also visible.
Matlock Bath : New Bath Hotel (4) | Matlock Bath: From the Heights of Abraham, the Changed Landscape

A list of people connected with the Royal Hotel, extracted from various Directories and census returns, is below. Coloured links take you to directory or census transcripts, where possible. If it doesn't say 'census', it was mentioned in a trades directory.

1881 Census - William Henry Ivaats (the address is not given in the census, but Mr. Ivaats advertised in Kelly's of that year). He subsequently moved to the Isle of Man but was living in Derby when he died on 18 May 1889. He was buried at Holy Trinity.
1887 - John Archibald Hinton, manager
1891 } - Royal Hotel, Thomas Tyack, proprietor
1895 }
1891 Census - Frances Elizabeth Hesketh Hotel Manageress
1899 - Thomas Tyack proprietor, and at Bakewell (by 1900 he was in Bakewell, where he died in 1907, aged 72)
1899 - Frances Sarah Lake
1901 Census - Eamy Frances Shaw, Hotel Manager (licence transferred in 1900)
1908 - Royal Hotel, A. Büttgen, manager
1912 - Thomas A Matthews
1914 - George Storey, manager^[1]
1916 - (see Private Residents) Howsin Miss Beatrice, Royal hotel journalist & newspaper reporter, Royal Hotel (Cecil G. Morris, manager)
1922 - Did Not Advertise
1925 - G. Brooks, manager
1928 - Miss Janet Finlayson, manageress
1929 - R. J. Bray, proprietor^[1]

Royal Hotel, from a photograph by Thomas Meredith Henshall (see Photographers), who was standing on the roof of the bath/pool to take his picture.

References:

^[1] "The Daily Telegraph," 14 Oct 1908 was just one of the newpapers to announce the fact that the new wing was open..

^[2] Beresford, Charles (2007), "The Bath at War, A Derbyshire Community and the Great War", Country Books/Ashridge Press. ISBN 978 1 901214 91 8. Several chapters are devoted to the time the Canadians spent in Matlock Bath.