It's a memorial to Charles Chesham (the 3rd Baron Chesham) who died whilst out hunting with the Pythchley Hounds on the 9th of Novemeber, 1907.
It's in a shocking state of repair, but as I reminded the other day, it's not surprising that it's in this state considering that in the past they knocked down the remains of the Northampton Castle to build a train station and what's left of the Eleanor Cross is also not as good as it should be with lots of the steps missing.