A class 7 vessel was a Starfleet designation for a type of interplanetary sublight spacecraft, used during the 24th century. These vessels are typically armed with lasers and were manned with a small crew of about two dozen. Overall, they were slightly faster than class 9 cargo vessels.
In the final draft of the script, the Atlec vessel was classified as a Squadron Class combat craft with a crew of 26. The ship was armed with phasers. As for the Straleb vessel, it was classified as a Class Four armed spacecraft. 
The term "class 7 vessel" would seem to indicate ability, rather than design, as the two vessels with this designation that appeared were of the same class, but significantly different design lineages.
The Merchantman model from The Search for Spock appeared as one of these two vessels; a new model appeared as the second. Footage of the second model would be reused for the Antares-class Corvallen freighter in TNG: "Face of the Enemy", and would later return, slightly modified, as the Angosian police shuttle vessel in TNG: "The Hunted".