We do not know much about this Hugh Beard. Each of the three brothers (Hugh, John, and Samuel) had a son named Hugh. In very early Greene County, Tennessee records, we find Lieutenant Hugh Beard listed in the Paymaster's List of that county. He served and was paid on the 10th of July and 29th of October in 1794.
Since the older Hugh was a major officer at this time, it cannot be his record. That Hugh and his brother Samuel both had sons named Hugh, but we know that both of them were born 1780-1790. They would have both been too young to be a lieutenant in the county militia. Therefore, this Hugh was almost certainly the son of John Beard.
We find no other records of this Hugh Beard so far. It does not appear that he moved to Adair County, Kentucky with the rest of the family about 1798. Serving in the militia in Greene County in those times was dangerous and it could be that he was killed or died before the family moved on to Kentucky.