With the caveat that I am not a lawyer; I'm a photographer, author, and artist who studies copyright law on occasion so I know what I personally can and cannot do...and what rights I hold to my own work:
I expect there is copyright permission to think about but what about public domain photo's of these famous celebrities? i have seen some recent Tarot decks used with famous faces one i can think of ( Marilyn Monroe, although the images looked like they were done by an out line pencil drawing and painted in a Pop art style? I expect many of these decks that use copyright images would of been created for private use only then sold on the bootleg market.
But it would be interesting to see if the Beatles Tarot was made available for public use.
There's some legal difference (at least in the US) between drawing a Marilyn Monroe image from an existing photograph and then selling copies of that drawing--even as Tarot cards, if you wanted--and directly using another person's images. Even drawing it can be dicey--it's *usually* considered different enough from the original to be safe, but not always. There's no perfectly clear cut rule of thumb around what actually constitutes derivative work, at least in the US...they try to quantify it by the percentage of difference, but the "iffy" cases I've read about very often seem to fall into the "I know it when I see it" category; what you can get away with often depends on a judge or jury's opinion of just how different your work is from the original. Manipulate it to the point where it's no longer recognizable as the original, and chances are it'll be confirmed as new art. But below that threshold, it can be dicey.
For an easy example of how thorny the legal concepts of fair use and derivative work can be, just check the discussions around the copyright issues of blog photos of your readings--there are several here on this site. Your own photograph of cards you pulled for a reading is yours...but it may or may not be legal to use on your blog, depending on a number of things (like whether or not it's being used in a commercial manner--on a blog that accepts advertising, for example), because it's not different enough from the original card you took a picture of. It's ALWAYS safest to seek permission of the copyright holder--in the case of this deck, the photographer or agency that holds the rights to each photo used.
Here's a link on collage work and fair use myths I stumbled across today that's rather interesting:
http://www.funnystrange.com/copyright/myths.htm
Apparently it's from the artist of the Victoria Regina Tarot--which made me laugh, since I wasn't actually searching on tarot decks and collage. I highly recommend going through ever page linked on the left; she's clearly studied the issue in depth. Note--she's not a lawyer either, don't rely strictly on what you read on the Internet to protect yourself.
My own take:
The minute you take something like a collage you made of photos that you "found on the Internet" from a personal use level to a for-profit product, you run a serious risk of being pursued for copyright violations. Legally, you violate copyright the minute you use unauthorized images to produce your own art, because derivatives are technically allowed only to the copyright holder and those they license to produce such things. Realistically, you're unlikely to be hassled for it when you don't put it out into the hands of the viewing public by publicizing it. Use images you didn't take yourself of someone high profile, add in anything related to their professional name, and then advertise your newly created wares for purchase on the Internet...well, some people like playing with fire, I guess. (And yes, the name of the band is probably trademarked, potentially in several countries, especially when used in conjunction with the likenesses of the band members.)
If you're going to illegally use something that doesn't belong to you, it's just smart to stay off the radar of people known for aggressively pursuing what they own and who won't hesitate to legally make your life miserable while (quite correctly) defending their copyrights or trademarks. Even the images of these cards as they stand right now could earn the creators a DMCA takedown from Word Press and Facebook if they don't hold the licenses to use all those individual photos--all that takes is one copyright or trademark holder contacting the site host, and no intent to profit from the use of the unauthorized images is even necessary.
Now, is that likely? Maybe not, so long as they're not trying to
sell a deck of these cards, or make multiple copies of them. There are plenty of artists and writers who won't go to the effort of going after their misused stuff on the web, because it's a neverending job to stay on top of it, or they simply don't care. But the copyright holders would be within their rights to pursue a takedown of the images utilizing their work, and to potentially sue for damages in some jurisdictions, even without a sale taking place.
Buying the for profit usage license to one or two photos, even iconic ones, might not be too outrageous. It's when you get into using lots of them, as this deck appears to, that it's likely to cost you far far more than you can make from it.
Really, the only true "public domain" photos that you can do whatever you want with, are those that have entered the public domain legally according to the appropriate dates for your home country. Many countries--not all!--use a rule of thumb where copyright begins on the date of creation & runs either 75 years, or follows the rule of the creator's Lifetime+75 years. By that rule, basically images shot in the 1950's or later are mostly not in the public domain yet, with exceptions only where copyright was essentially released by the holder. (US laws are less straightforward than some thanks to Disney managing to get them tweaked repeatedly to protect their copyright over Mickey Mouse--I believe currently anything created after 1928 is still protected, though I'd have to check that date. Beatles pics taken by US photogs are almost certainly still under copyright. Another thing to consider is that some of those Beatles pics may be governed by UK/European laws, others by US--was the image shot here or there, released on which side of the pond first, by a photographer from which country? At that point, I'm not sure whose rules apply...or is it strictly the rules of the end user's home country? Ugh. Potentially very messy.)
Of course, anything that artists have licensed under Creative Commons licenses are fair game for others to work with, that's the point of CC in the first place...
subject to the limitations of the license they chose to use. Some don't allow any manipulation of the original creation at all. Others may specify certain terms--non commercial use, for example. I made a set of derivative app icons a while back, based in small part off someone else's free, but CC-licensed set. By the license they chose, my own derived work was limited--not only did they have to be credited and the originals linked, but I was legally obligated to release my own work for free under the exact same license--I couldn't modify the license, nor could I charge for my 90% different version of the icons. Which was fine...I'd done my homework going into it & was doing it for fun...but it did mean forgoing any chance of making money off many hours' work myself.
The OP here would be smart to consult a copyright lawyer in their country before proceeding with this with any intent of anything beyond personal use. And even if approved somehow without further legal issue in their own country, don't assume it's legal to sell the final product in any other...laws can vary widely.
Honestly, if it were me? I'd probably check in with the representatives of the two estates & with Paul & Ringo's marketing teams, pitch it as an homage to the band, and see if there was interest there. If they backed the project, a LOT of potential legal and even financial headaches would all but vanish, and they have thousands of pictures from that timeframe already under their control or licensed for use. If any of them refuse, you have your answer.