I have so far found 2 George Sinclairs whose occupation is given as “Professor of Music” in the 1901 Census:
1901 census
RG13 Piece 4984, Folio 46, Page 8
15, Hamilton Street, St John, West Cardiff
SINCLAIR, George, Head, Married, 29, Professor Of Music, born Cordon, Isle of Man
SINCLAIR, May F, Wife, Married, 23 born Glasgow, Scotland
1901 census
RG13 Piece:2480 Folio:123 Page:10
20, Church Street, Hereford St John The Baptist
SINCLAIR, George R, Head, Single, 37, Professor Of Music, Croydon, Surrey
DEVONALD, Martha E, Servant, Single, Housemaid (Domestic) Swansea, Glamorganshire
DAVEY, Eliza, Servant, Single, 50, Housekeeper (Domestic), born Kea, Cornwall
I believe the second of these records can perhaps be eliminated because it seems to refer to George Robertson Sinclair who was the organist at Hereford cathedral and a friend of the composer Elgar. This George Sinclair did not marry and died in 1913 1917.
However the first record could relate to “your” George.
In 1911 there is a George Sinclair, Professor of Music, living in West Cardiff. He is shown as age 38, born Tooting, Surrey and married with a son George, aged 7. Although George Snr is shown as married there is no wife listed and I have not been able to find May F. Sinclair in the 1911 census.
Have you investigated these records?