Does a non-extinct gliding species of bird exist?
There is a classification of birds called Soaring birds.
Soaring Birds

In definition, some land birds, such as vultures and certain hawks,
sustain flight for long periods without flapping their wings. They
take advantage of updrafts produced when the wind blows over hills and
mountain ridges or make use of rising columns of warm air called
&quot;thermals.&quot;
Vultures stay within thermals by flying slowly in tight circles. They
have short, broad wings and a low wing loading (ratio of bird weight
to wing area) that allows them to remain aloft and to be highly
maneuverable at slow speeds. [1]

List of soaring birds

Birds of Prey

Buzzards
Condors
Eagles
Falcons
Harriers
Hawks
Kites
Osprey
Secretary Bird
Vultures


Passerine

Chough


Cranes

Sandhill


Sea birds

Albatrosses
Frigatebirds
Gulls
Herons
Pelicans
Petrels
Shearwaters
Storks
Terns


Extinct

Argentavis



Buzzard

Chough

Sandhill

Albatrosses

(source: scienceviews.com)
Argentavis[Extinct]

(source: mnn.com)
Update:
Most similar morphology to Archaeopteryx is found in Hoatzin (Opisthocomus hoazin) like claws as hands as they hold the branch when they are small.

(source: pbworks.com)
Source:
[1] Soaring Birds by Paul R. Ehrlich, David S. Dobkin, and Darryl Wheye.