Hard to say without actually hearing the bike running. Does the bike have fresh oil, and the right oil level? Have valve clearances been adjusted recently? Does the noise disappear if you pull the clutch in, in neutral?
Don't forget the Triumph has a L O N G camchain to get all the way to the top of those tall cylinders.
As the bike has an auto camchain tensioner, they can sometimes sound a little noisy if the tensioner is 'between clicks.' You may find that after a good long run when the engine gets thoroughly warmed up, the rattle will disappear as the tensioner's spring mechanism will have taken up all the slack.
I have a Suzuki SV (another bike with long camchains), and this is a common question from new owners of those. The answer as far as the SV goes is, they all do that, sir.
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