No record of his death on FreeBMD but he may have d. in Ireland.

His entry in Alumni Dublinenses (pub 1924) is:
  “HAMILTON, HANS HENRY, S.C. (Dr Nichols) May 18 1816, aged 15; s. of Henry Generosus; b. Dublin.  B.A. AEst 1820.  M.A. Nov 1832 [Irish Bar 1823; Q.C. Chairman of Co Armagh.]  See Boase.”

The Irish deaths register has three Hans Hamilton deaths on record between 1870 and 1890:

Death year  Quarter  Age  District

1880          3       97  Banbridge
1888          2       85  Downpatrick
1890          4       84  Lame

And for Hans Henry Hamilton from 1870 to 1895, there is this one record:

Group Registration ID N/R
SR District/Reg Area Dublin South
Deceased Age at Death 74
Returns Year 1875
Returns Quarter 2
Returns Volume No 7
Returns Page No 560

I am inclined to think this has to be him and that Burke’s LG had a transcription error of ten years.

This is all confirmed in his probate index entry for his English estate at the York office.
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His probate index:

HAMILTON Hans Henry Esq
18 December
Effects in England.  Under £1,500.
Probate of the Will of Hans Henry Hamilton late of Fitzwilliam-place in the City of Dublin Esquire Q.C. who died one or about 20 April 1875 at Fitzwilliam-place granted 3 September 1875 at Dublin to Edward Nicholas Hill of Larlandrive Cotting in the county of York Esquire one of the Executors.

Edward Nicholas Hill was his son-in-law, married to his daughter Frederica Mary.
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The Hurst marriage register has been transcribed as:

Hurst Village Parish Registers

Marriages 1825-1849
Surname Christian name Of Notes Parents Witnesses  Date

Wetherall Augusta Hurst spinster           Rogers Wetheral   Apr-12-1833
Hamilton Hans Henry St Anne Dublin bachelor esquire  Mary Wetheral     by licence
      Augustus W Wetherall
      Jarrianne Gardner
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