Thank you for the photo. It is regretably too small to permit a full ID.
Double breasted frock coats - meant to be worn in everyday ordinary duties - were introduced in the Royal Navy from 1847, but the one illustrated may date from the end of the 19th century. These were to have buttons at the cuffs. Rank stripes at the cuffs with the executive curl were introduced in 1856, and were further defined in the 1860s and 1870s insofar as the number of stripes, etc.
In the case of this coat, the rank is either Commodore 1st Class or Rear Admiral (one cannot tell from the details of the epaulettes). By the 1891 regulations, the cuff buttons were removed (except for Warrant Officers) and the frock coat became dress items, being replaced by the shorter "Monkey Jacket" still worn today.The Frock coat was redesigned in 1933 to have four buttons at each side.
I would need to see a button and an epaulette to comment further.
So, for now, from what I can see, a Commodore 1st Class or Rear Admiral, c. 1891-1933.
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