I'm pretty sure this would be St Helena in the South Atlantic. As others have said, there was a British army presence there during the late C18th and C19th.
There are some records for St Helena here in UK.
Firstly,
www.1837online.com has the overseas BMD indexes. In the army chaplain and regimental indexes you will find various persons of the name Clark born in the first half of the C19th -- e.g. Frederick born 1818, Elizabeth 1837, Emily M 1839 etc. if you find any you like the look of, you can then apply for the birth certificate itself online via the GRO.
Also, the former India Office collection now in the British Library has British baptisms, marriages and burials on St Helena from 1767-1835.
Finally, there are also materials at TNA in Kew, for instance at shelf refs WO12 and WO97. You can check search the catalogue online here: http://www.catalogue.nationalarchives.gov.uk/search.asp