The phrase "a tireless quest" is correct and usable in written English.
It can be used to describe an ongoing and persistent search or pursuit of something, often implying dedication and effort.
Example: "Her tireless quest for knowledge led her to explore various fields of study and research."
Alternatives: "an unending pursuit" or "a relentless search".
He achieved all he did by his amazing energy and a tireless quest for perfection.
But it was a surprise to discover Amis claiming, in "The Moronic Inferno," that between 1950 and 1980 Norman Mailer was engaged in "a tireless quest for a fistfight" (surprising that Amis used the t-word, I mean, not that Mailer was so desperate for punch-ups).
Peggy Say, who spent nearly seven years on a tireless quest for the release of her brother, journalist Terry Anderson, and fellow hostages from kidnappers in Lebanon, died Wednesday.
The arrangement will obviously be mutually beneficial: Victoria will bring her unrivalled musical expertise to the show, while she in turn will be given an invaluable boost in her tireless quest to make it in the US by being beamed into literally a gazillion American homes.
Nabbing federal or state funds can be an exhausting gauntlet (check out "One Energy start-up's Tireless Quest For Capital"), but at least the government doesn't charge interest or demand control.
In his tireless quest to dazzle, the man who founded the Ballets Russes in 1909 drew the brightest artists of the era into his orbit.
In his tireless quest to wean England from meat in the early 18th century, the famously corpulent Dr. George Cheyne set out to poison the novelist Samuel Richardson.
John McCain and these extremists who have signed this letter are the very people who have done nothing but block and obstruct, unyielding in their tireless quest to put moderate Republicans on the endangered species list.
Others still, such as Macierewicz, deputy leader of Law and Justice, have expanded their political careers around surviving twin Jarosław Kaczyński's tireless quest to disprove claims that his brother put undue pressure on the pilot, Arkadiusz Protasiuk, to land, despite atrocious weather conditions.
I'm not sure it even noticed; merely swam off on its own tireless quest.
In Amazon's tireless quest to take all the pain points out of shopping — and make you buy as much as humanly possible, the mega retailer is utilizing Alexa to push out holiday shopping deals.
