Atmosphere's song The Waitress could be seen as a sequel to Her Music Box, with the little girl in the latter having grown up.
Guitarist Jerry Cantrell's second solo album, "Degradation Trip", has been described as a spiritual successor to Alice in Chains' Dirt album.
Chickenfoot is this for Van Halen, considering half of Chickenfoot is comprised of two former Van Halen members. They musically resemble the David Lee Roth years, which is ironic, because they feature Roth's replacement Sammy Haggar on vocals.
So many of Frank Zappa's albums were this to each other, it would take a lot of space to list them all.
Tom Waits' "Swordfishtrombones" was the precursor for "Franks Wild Years" [sic], which was followed by "Rain Dogs". Collectively, they are known as the Frank O'Brien Trilogy.
Pink Floyd's "The Final Cut" is seen by many to be a successor to their earlier album "The Wall". Both are concept albums dealing with pain, loss, and detachment.
Also a rock musician who appears in some of the album's songs may be Pink.
The Wall and The Pros And Cons Of Hitchhiking were written as part of the same set of 1978 demos, and both would have been considered to be the successor to Animals. The Wall won. The Final Cut began as new tracks written in 1982 for The Wall movie, along with rejected songs from the album's 1979 sessions, but only "When The Tigers Broke Free" was used. It was to be released as an album called Spare Bricks. It was later completed with new tracks about and a new concept about the schoolteacher from The Wall being angry about The Falklands War and warmongering in general and called The Final Cut. TPACOHH was renewed as Roger Waters' first solo album. As a result, the albums have similar sounds and similar subject matter.
Roger Waters' solo album Amused To Death has been described by some fans as on par with Pink Floyd's classic albums. Executives at Roger's label apparently admitted as much to him, saying that it would have sold many more copies if it was a Pink Floyd album.
Amused To Death was actually written at first as, literally, a sequel to Waters' Radio KAOS album. Roger's objections to the first Iraq War (and its depiction by the news media as it unfurled) changed all of that.
Lady Gaga has been called the spiritual success to Cyndi Lauper.
And Madonna. And Dale Bozzio (whose hair style she admitted to copying). There are many who believe Gaga is just playing the system and is writing the sort of music that is popular whilst not taking it too seriously.
Heaven and Hell was the Ronnie James Dio line up of Black Sabbath when Black Sabbath returned to its original Ozzy-led lineup.
When 16 Horsepower started drifting apart, the frontman and primary songwriter started recording and performing under the moniker Woven Hand, basically picking up exactly where his first band left off.
Britney Spears is considered to be the 00's successor to Madonna. Noted on her Wikipedia page, by the clear majority.
Porcupine Tree is, according to critics and lots of fans, the spiritual successor to King Crimson. Hell, even frontmen from both bands (Steven Wilson and Robert Fripp respectively) agree on this!
Hardly surprising, then, that Fripp actually invited Wilson to supervise the remastering of King Crimson's albums.
The Foo Fighters are without a doubt the spiritual successor to Nirvana. Dave Grohl was a member of both bands, and the Foo Fighters' first album was widely stated to sound almost exactly like Nirvana.
The reason for this is most of that album was recorded in 1992 when Grohl was a member of Nirvana and so was influenced by what they were doing at the time. In fact some of those songs were written for Nirvana (This Is A Call being the most obvious one). Cobain liked Grohl's songs and wanted to use more of them (just Marigold got recorded as a B Side) but never got round to it.
Green Day's concept album "21st Century Breakdown" is almost a direct sequel to their previous rock opera "American Idiot." One could go as far as to argue that this could go beyond spiritual successor, as they both take place around the same time, deal with the same basic themes, and have very similar characters.
Several of the songs from 21st Century Breakdown are featured in the American Idiot stage show.
David Bowie's Aladdin Sane is this to his previous album The Rise and Fall of Ziggy Stardust and the Spiders from Mars. He wrote some of the songs for it while on the U.S. tour supporting Ziggy Stardust, and keen to wean himself from the Secret Identity Identity issues surrounding the Ziggy persona, he came up with a Ziggy expy who was suffering a mental/emotional decline as he journeyed across America.
Arch Enemy's early albums (Black Earth, Stigmata, and Burning Bridges) have all been described as a continuation of sorts to Carcass's sound from the time of their fourth album, Heartwork (which Arch Enemy's lead guitarist, Michael Amott, played on).
Arcade Fire is one of these for Neutral Milk Hotel for some. It doesn't help that Arcade Fire signed to Verve Records because Neutral Milk Hotel was part of the label.
Sun Kil Moon is the Spiritual Successor to Red House Painters. When Mark Kozelek attempted to get RHP back together in 2002, their music had changed to drastically that he considered the project a separate one and renamed it to Sun Kil Moon.
Tribute might very well be this to The Devil Went Down to Georgia.
Mike Oldfield's 1990 album Amarok is this to his 1975 album Ommadawn.
Lamb Of God's 2012 album Resoultion is considered by some to be one to Pantera's 1997 album The Great Southern Trendkill in terms of both the dark, depressing and frightening tone and style of both albums. Hell, just compare Lamb Of God's "King Me" with either Pantera's "Floods" or "10's", both styles are alike!
A lot of solo musicians' careers become spiritual successors to their bands after they break up.
A number of critics have cited the Stevie Nicks/Lindsey Buckingham-led Fleetwood Mac as a spiritual successor to The Mamas and The Papas, since they were both Californian pop-rock bands with tight male-female vocal blends.