The D4 class was armed with two torpedo launchers on top of the wings near the fuselage. The engine had a single aft exhaust. The wings could be angled in various ways, giving the ship high-speed atmospheric maneuvering capabilities and allowing it to maneuver through tight spaces. The ship had landing capabilities. Troops from the ship could also be deployed on cables mid-flight from four hatches in the underside of the craft. (Star Trek Into Darkness)
In 2259, three of these vessels intercepted the K'normian trading ship that was confiscated by the crew of the USS Enterprise during the Mudd Incident. The trade ship was carrying James T. Kirk, Spock, Nyota Uhura, Hendorff and another security officer over the Ketha Province on Qo'noS. The D4 class ships forced the trade ship to land. Two of the ships were destroyed by Khan Noonien Singh with a boolean gun. (Star Trek Into Darkness)
Concept artist James Clyne designed the original sketch for the D4 class Klingon fighter. Visual effects artists at Pixomondo heavily detailed the industrial-type fighter ship design. Their refinements of the class came from extrapolating how it might look, based on how they envisioned Qo'noS to look in Star Trek Into Darkness. At Pixomondo, the D4 class was modeled by CG Supervisor Enrico Damm and Compositing Supervisor Dan Cobbett, rendered in V-Ray.
The Pixomondo team gave the D4 class a "Bird-of-Prey" feel.  Alex Kurtzman said about the Bird-of-Prey, "You can't really reinvent the basic shape of it. You can update it in a way that's consistent with the way we've updated the rest of [Star Trek], so there's a highly militarized take on it. It was always militarized, but even more so now." 
Pixomondo Visual Effects Supervisor Ben Grossmann has stated that the ship was designed “not in the traditional namesake of the Klingon Empire, but more of like […] a bad-ass predator. You had this larger more predatory hawk." Grossmann also regarded the Klingon ship as slightly less "nimble" than the trading ship. 
Pierre Drolet designed another version of the ship, which more closely resembles the prime reality's Klingon Bird-of-Prey. It was rejected by the film's art department before he finished modelling it, but he opted to complete it after receiving requests from fans who looked at the unfinished version. 
In "Unexpected", Vorok's battle cruiser was originally designed by John Eaves to be a prime universe counterpart D4-class starship. However, the K't'inga-class CGI model was reused to represent the ship when it appeared in the episode.
In Countdown to Darkness, Issue 4, a Klingon starship with a very similar hull configuration was shown as a much larger ship which approached the size of a Constitution-class starship. In Manifest Destiny, Issue 2, the IKS Chonnaq had several of these vessels assist in attacking and boarding the Enterprise.
Star Trek Online released a version of this ship during the release of the third expansion Agents of Yesterday. Classified as the "Kelvin Timeline D4x Pilot Bird of Prey", the ship was similar to the D4 introduced in Countdown into Darkness, but is scaled up to be roughly the size of a Bird-of-Prey. It is also an enemy ship that players must face off against in the mission "Terminal Expanse".