One of Sega's official blogs puts the XBLA and PSN port of the arcade game—both handled by development team AM2—for a spring release in Europe. The ESRB has just rated the game E10+, so a North American release is similarly imminent. The game has not yet appeared on Microsoft's official schedule for upcoming XBLA releases.
But we'll be playing After Burner Climax at some point in the coming months, happily reviewing the high speed arcade dog fighting game for Kotaku.
After Burner Climax Is Coming! [Sega Europe Blog]