The Quest was released in various formats, including CD, LP, Blu-ray Disc, and on streaming platforms, and reached number 20 on the UK Albums Chart.

[5] This marks the first Yes album to involve Sherwood as a musician (he had mixed Heaven and Earth) since The Ladder (1999), who replaced original bassist Chris Squire following his death in 2015, and the first without any founding members.

[11] A typical scenario involved one member contributing an instrumental section for a track, which Davison would then take and develop vocal lines and lyrical ideas.

[11] Howe approached the writing process with caution, which he had also done for Fly from Here (2011) and Heaven & Earth, to ensure the songs were fully arranged and to every members' satisfaction prior to recording.

[8] The album was recorded in two main locations in 2020 and 2021; White and Sherwood put down their respective drum and bass parts first at Uncle Rehearsal Studios in Van Nuys, California, and Schellen contributed percussion.

After sharing the recording files to the group online, and once COVID-19 restrictions began to ease, Davison travelled to England to join Downes and Howe at Curtis Schwartz Studio, where the album was completed.

The parts were written by English composer and arranger Paul Joyce, a longtime fan of the band who had produced orchestrations for Howe's solo album, Time (2012).

[19] On the following day of its release as a digital single, Downes addressed rumours that the song's riff was similar to "The Dawn of an Era" by English composer Francis Monkman.

[20] The opening keyboard riff has been compared to "Fanfare for the Common Man" by Aaron Copland and adapted and played by Emerson, Lake & Palmer.

[8] "A Living Island" was inspired while Davison spent time during lockdown in Barbados, where he "really did some soul searching" on its lyrical message: "I felt the need to express in words all those intense thoughts and feelings and my personal perception of it all.

He called it a "grandiose theme" that has "big major chords" in a similar style to Yes tracks "And You and I" and "Awaken", and thought it was a good way to close the album.

[11] The Quest was announced on the band's official website, YesWorld, on 7 July 2021, revealing the track listing, artwork, and scheduled release date.

He picked "The Ice Bridge", "Dare to Know", and "Mystery Tour" as distinct songs that stand out from the rest, which is "synth-heavy and cinematic, light on hooks and riffs, without choruses that will linger in your head".

[29] Geoff Bailie of The Prog Report said that the album "sounds like the work of a new lineup, with a new approach" and praised Howe's "beautifully rich guitar textures" throughout.

[31] Ultimate Classic Rock reviewer Michael Gallucci wrote that with The Quest, the band "dips into the nostalgia pool once again" and "goes through some familiar motions."

Though he said the album "starts in the right place" with "The Ice Bridge" and "Dare to Know" sounding like "classic Yes", it begins to get "even more self-serious and metaphysical in its musings" with "Minus the Man" and "Future Memories".

He argued that Sherwood had proven to be a proficient replacement for Squire on stage, and his "running basslines and trebly undertones" provide a good basis for Howe and Downes to riff off each other.

Kenney hailed "Leave Well Alone" as "a true Yes classic in the making" and "The Western Edge" a high point on the album, though despite "A Living Island" the least "Yes sounding" track it is also a strong moment.