Having been made a baron for the Battle of the Nile, and a viscount for the Battle of Copenhagen, the next step up the ladder would have been to make him an earl.
Following Trafalgar, Britain had few engagements in the Mediterranean, and so Nelson's time would presumably be occupied by enforcing the blockade.
By 1805 Nelson was suffering recurrent bouts of ill-health, most likely bouts of malaria, in part exacerbated by the numerous wounds he had suffered. It would not be a great surprise if he, like admirals Collingwood and Cotton, died before 1815.
If he returns to England alive, he probably lives out his days in the Lords, which he frequently attended during a period of recuperation between 1801 and 1803. Politically he seems to have been a Tory, but doesn't appear to have the political abilities or inclinations of Wellington, so is unlikely to ever do more than sit. Also, his scandalous personal life, here not covered behind his martyrdom at Trafalgar, will count against him in political circles, so political figures will distance themselves from him.