I'm looking for photos / sketches / portraits of him for the CPS project's history book. A Barrister, he was appointed as second Police Magistrate (the position previously called "Assistant Magistrate") in 1862. He left Hong Kong in 1870 , but I'm not sure if he carried on as Police Magistrate that long, as E W Goodlake was appointed as Second Police Magistrate in 1867.
Ok, the 1867 end-date is confirmed:
Of the Irish bar, called in Michaelmas Term, 1847; was previously Police Magistrate and resigned to take private practice in February, 1867. 
He gets the following mention in COLONIAL HONG KONG AND MODERN CHINA: Interaction and Reintegration, quoting  as its source:
J. C. Whyte, graduated from Trinity College, Dublin, was called to the Bar of Ireland in 1847, appointed second police magistrate in 1862, acting judge of the court of summary jurisdiction in 1863, 1866, 1869, and a provisional member of the legislative council in 1866, died in 1871. See Norton-Kyshe, op. cit., Vol. 11, p. 39, 51, 81, 172, 174, 177.
There aren't any results for whyte in the photo search at HKPRO, and he didn't serve with Legco. No relevant results for whyte hong kong in the UKNA.
I haven't found any mentions of him in family trees.
- Both mentions come from History of the laws and courts of Hongkong. Whyte isn't mentioned in the book's index, though the relevant entries appear in a Google Books search.
- Appendix III of History of the laws and courts of Hongkong: http://archive.org/stream/historylawsandc00nortgoog#page/n23/mode/2up