From the look of this page I suspect it is from St Helena?
There are a couple of slave burials on the page, which also matches St Helena.
Whether it is St Helena or not, it is clearly a place with a significant military presence.
The entry is saying that George Esse belonged to a Company of soldiers under the command of a Captain Hamilton.
The next four entries are men from other Companies under different command.
Further down, Richard Evans is from the 84th Regiment.
I'm going a bit out on a limb here, but I think the Companies identified by the Captain's name are East India Company units, as opposed to official British Army Regiments.
The East India Company maintained a significant military force organized in much the same way as the army of a nation state.
George may have been an infantryman, an artilleryman or potentially an artisan of some type. There was at least one Company of Artificers on St Helena at the time, although under different command.
You would have to search on the internet for the Captain's name & the place to (with luck) find more.
If it's not a place run by the East India Company then disregard this last section (the out on a limb bit).
The note at the side reads:
in former Entry - with Exception of John Perkins
vide Page 71
My guess is that the entries constrained by the bracket have been transcribed from another source. You could go back to Page 71 to see what he is referring to (vide means see here).