At first glance, it certainly seems odd to have Clarkson hosting a program on the BBC just weeks after getting the boot by the network. However, a network spokesperson clarified things to BBC News, saying: "Jeremy's contract has not been renewed on Top Gear but he isn't banned from appearing on the BBC."
Have I Got News For You is a show that invites a panel of guests to make humorous observations about current events and politics. Clarkson has hosted there several times and actually had trouble once before. According to BBC News, while presenting in 2008, he threw a pen at a guest causing a cut to the person's face.
Given Clarkson's general inability to keep his mouth shut about anything that's even slightly controversial, his first return to hosting on the BBC should be rather interesting. It's hard to imagine Clarkson not making some comment about his predicament over the last few weeks... but we'll just have to wait and see.
UPDATE: It looks like Jezza is not returning to the BBC after all. At least not yet. The Mirror reports that Clarkson won't be on the April 24 broadcast of Have I Got New For You but will pick up hosting duties later this year, according to the managing director of the show's production company.