(covers information from several alternate timelines)
A deep space vessel was any type of starship designed for extended travel in deep space. As the term was relative to the level of technology and what was defined as "deep space", sleeper ships were an example of early deep space vessels.
In an alternate timeline, following Chakotay and Harry Kim's successfully returned to Earth in 2375, aboard the Delta Flyer, and at the cost of the loss of USS Voyager, Kim experienced incredible survivor guilt. He signed onto the first deep space vessel he could find, in order to locate Voyager. They searched for four years, but Starfleet Command called off the search in 2381, citing a "low probability of success," forcing Kim to ultimately resign Starfleet and pursue the search on his own. (VOY: "Timeless")
Following Starfleet's contact with Voyager the following year, Admiral Hayes, informed Captain Kathryn Janeway that they had "redirected two deep space vessels toward your position" in the Delta Quadrant. Hayes added, that "if all goes well, they could rendezvous with you in the next five to six years." (VOY: "Life Line")