In 2373, Hayes contacted Captain Jean-Luc Picard aboard the USS Enterprise-E to inform him of the incursion of a Borg cube into Federation space. Over Picard's objections, Hayes then ordered the Enterprise-E to patrol the Romulan Neutral Zone as Starfleet mobilized to intercept the cube, feeling that Picard's previous assimilation by the Borg would be a disadvantage in the confrontation. Picard later decided to break with his orders, however, and ordered the Enterprise-E to Earth to join the battle. Picard subsequently took command of the fleet when Hayes' ship was destroyed. (Star Trek: First Contact)
In 2374, a message from Hayes was included in an encoded data transmission sent to the USS Voyager through the Hirogen communications network. When initially received, Harry Kim needed some time to decrypt this message. (VOY: "Hunters") Decrypting the message took much longer than anticipated, and with the apparent help of Arturis it was later deciphered. However, it was later determined that what Arturis deciphered was a forged version of the "decoded" message, which led the Voyager crew to the fake Starfleet vessel USS Dauntless. Captain Kathryn Janeway was subsequently able to retrieve part of the real message from Hayes expressing his condolences over their situation, and thus exposed Arturis' ruse. Janeway described Hayes as a "good man, fine officer, a bit of a windbag." (VOY: "Hope and Fear")
In late 2376, Admiral Hayes sent another message to the Voyager after regular communications were established through the MIDAS array, informing Janeway that they had dispatched two deep-space vessels towards the Voyager's position and requesting information on the ship's mission and status of the Maquis. Janeway was troubled that Starfleet still saw the Maquis as a separate entity, since she now considered them all part of her crew. (VOY: "Life Line")
Background information Edit
Admiral Hayes was played by actor Jack Shearer, who previously appeared as another admiral, Admiral Strickler. The voice of what was also presumably the vice admiral in "Hunters", was voiced by an unknown actor.
In the first draft of the script for Star Trek: First Contact, during his initial conversation with Captain Picard about the Borg invasion, Hayes tells Picard "The new quantum torpedoes are doing the trick, Jean-Luc. We've destroyed forty-seven Borg ships so far... and only lost fifteen of our own." In contrast to the final film, he then goes on to request Picard's assistance in destroying a Borg sphere that has broken through the lines wishing him "Good hunting." Near the end of the film, after the Enterprise-E has returned to the future, Picard is again hailed by Hayes who states the crew had disappeared from sensors momentarily. He then proceeds to ask Picard if they are alright, to which Picard replies, "We're fine, sir. It will take some... time to explain." 
In the Star Trek: The Next Generation - Slings and Arrows eBook The Insolence of Office, following the attempted coup by Admiral James Leyton in 2372, Hayes is assigned to a key position within Starfleet Strategic Command. One of his first decisions in that role is to classify Lieutenant Commander Geordi La Forge's VISOR as a security risk, forcing him to undergo ocular implant surgery. The book also makes references to Hayes having least one granddaughter and two great-grandchildren as of 2372.
The Enterprises of Great Pitch and Moment ebook reveals Hayes was responsible for ordering the USS Defiant to the Battle of Sector 001, giving command of the ship to Worf and specifically ordering Captain Benjamin Sisko to remain behind on Deep Space 9 due to his previous experiences with the Borg.
Hayes is also featured in the Star Trek Customizable Card Game.