According to a report published by BBC2 boss Kim Shillinglaw the remaining three episodes of series 22 of Top Gear will be aired this year, most likely during the summer. As you can imagine there won’t be any studio scenes as BBC usually records those parts several days before airing the episode so it is obviously they weren’t able to do that because of Clarkson.
As you may have read, after the Clarkson fracas, James May and Richard Hammond were asked to film the scenes without their colleague but the two refused. Currently, BBC is trying to find a replacement for Jeremy Clarkson and Sue Perkins looks like a pretty good option.
However there is a small problem because we don’t know if May and Hammond will sign again with BBC. But the British national TV program is confident and will keep going the Top Gear show. For short Top Gear is dead! Long live Top Gear!

Source: BBC