There are some snippets of information on the Star Trek official website as well as some of the Extended Universe novels.
Origin: Shelia star system. A technological, non-humanoid life-form of
classification R-3; in appearance, a wrap of black, mucous-secreting
folds appearing as at least a head and gesturing upper appendages (not
too unlike the look of the creature Armus on Vagra II). As a culture,
they view humans as a lower life form and have no qualms about
exterminating those legally in their way -- as with the unknowing
human "trespassers" on Tau Cygna V. They have learned several United
Federation of Planets (UFP) languages but still consider them
imprecise. The Sheliak language continues to elude Federation
linguists, and even telepaths have been of no help. In face-to-face
dialogue with Captain Picard and Counselor Troi, the Sheliak ship
director speaks English without apparent translation aids. His
reception room is very large and open, perhaps indicating that space
is not critical on the vessel.
The Breen and the Sheliak don't share mutual borders but have disputes over various regions of space. Their ships and technology are apparently comparable.
A few minutes later, the results were on the screen, and Picard
grunted in dismay. “They could hardly have picked a worse place for
it. If I recall my Starfleet intelligence reports, that region of
space is disputed between the Breen and the Sheliak.”
“I’m not familiar with either.”
“They’re both very mysterious to us, in fact. But one thing we do know
is that they’re both very forceful about defending their territorial
claims. And neither would respond well to Federation intrusion, even
in a border zone.” The region in question, out past Albireo, was in
fact well beyond the far border of the Breen Confederacy, but they had
been establishing “protectorates” there for decades, expanding
aggressively to spinward since their antispinward expansion was
blocked by the Federation. The Sheliak’s borders and buffer zones were
well defined by the terms of the Treaty of Armens, but the Breen had
not signed that treaty and did not honor it.
First contact with the Sheliak happened some time in the 2250s or 60s
But the white-haired admiral smiled, looking for a moment like the
grandfather he was. “It’s all right-I can forgive it from a civilian.”
His kindly mien faded as his eyes darted in Picard’s
direction-specifically at his collar, where the rank pins would be if
he were still in uniform. “Of course you understand my problem with
what you propose. Relations with the Breen are tenuous at best
and-well, we’ve had no actual relations with the Sheliak for a hundred
years, and I wouldn’t like our next contact to be a military one, let
alone one we precipitated.”
The Sheliak have their own temporal security agency. It's described as highly efficient.
“Exactly. Some of the leading theories focus on the Carnelians, a
civilization as advanced as your own, more than capable of pulling it
off. But since the changes in their history didn’t unmake the defense
grid, their role must not have been the pivotal one. The Sheliak have
been under attack too, but they’d never deign to tell you, and their
own temporal agency is . . . highly efficient, so they’ve escaped
significant change. And the Typhon Pact . . . well, you can try
getting those stories out of Revad if we get out of here alive.
The Sheliak maintain commercial relations with other worlds but are known to be highly xenophobic about their contact with those outside their own species
“The first is a Sheliak commercial freighter. Given their extreme
xenophobia, I would think it highly doubtful that they would offer
Doctor Bashir, or any non-Sheliak, transportation to Andor, or to
Nog acquires a Sheliak shield modulator. It improves defence against radiation at the cost of defence against directed fire. Note that Keith DeCandido's editor doesn't know how to spell Sheliak and gets it wrong in several books.
Nog held up an isolinear rod he'd been carrying. Vaughn peered at the markings, and saw that it contained a replicator pattern. "I, ah, have something that might help. It's a shield modulator that I—acquired from the Shelliak."
Everyone whirled and stared at Nog. Dax's mouth was hanging open.
Bashir asked, "Aren't the Shelliak among the most xenophobic species in the galaxy?"
"Xenophobic's the wrong word," Dax said. "More like xeno-disdainful. They don't really fear other species, they just don't think all that much of them."