I've done a bunch of research on this, so I'd like to just share all the info I found on the track.
If anyone knows any more info, I'd love to know!
The History
In March of 2013 it was confirmed that Mark Ronson, a DJ at Paul's wedding had worked on 3 songs with him for the New album, two of these had been confirmed to be Alligator and New , but the other track was teased as "Life of a Party Girl"
Someone Steve Hoffman later noted "Maybe the Secret Life of a Party Girl was in fact Frank Sinatra's Party." but this can't be true due to the dates and studios this song was recorded, although maybe the track was reworked into Frank Sinatra's Party (although due to Frank Sinatras Party being written in the mid 70s, and Secret Life of a Party Girl being partly written by Mark Ronson, this also seems unlikely).
No news came from the songs until Sept 9th 2013, when MaccaReport reported a track list for the album, this site is sourced by multiple sites to be the source of the list.
When I emailed MaccaReport on how they found the tracklisting they stated
I'm unsure if this is how they found the track listing in 2013, or if they simply googled the song and found the forum post I referenced.The song was on the Japanese release… but was removed when they released second edition.
The tracklist noted "The Secret Life of Party Girl" was 6:15, which matches exactly with the tracklisting for Get Me Out of Here medley on amazon uk (this will be important for later.), at this point, Paul still could have been considering the track, or perhaps it was an error.
On September 23rd the album had been posted on Amazon
- the US had Bonus tracks "Turned Out", "Get Me Out of Here", and "Scared" as a hidden track for Get Me Out Of Here (totaling 6:15 length)
- Japan had the same but also included the bonus track "Struggle"
- the UK had Bonus tracks "Scared" and "Secret Life of a Party Girl"
However, according to a forum post this UK tracklisting was changed on to the US tracks on Sept 25th, which leads us to believe Paul either quickly changed his mind, or more likely this was a mistake (maybe they did want unique editions in each country though), amazon often does make mistakes like these.
Which brings us back to this forum post about the audio sample. I've combed through wayback machine and can't find any reference to this sample. I have 3 ideas for what this forum user could be saying
1. The sample never existed on Amazon and this was a memory error
2. The sample did exist and has since been lost
and in my opinion the most likely
3. The user did hear a sample, but the sample wasn't for Secret Life of A Party Girl, it was for Get Me Out of Here, amazon had simply put the wrong name for the track, and this goes in line with what we know about them "having the same length", it also makes sense with him thinking the sample was incomplete, since Get Me Out of Here, especially the Amazon Sample, sounds very rough. Someone refuted this point, saying the forum user would surely know what Get Me Out of Here sounded like by the time he posted that comment, however enough time had pasted that I think its likely he forgot what that short low quality sample (which he noted he didn't even like) sounded like, you can hear the Get Me Out Of Here sample here.
(also to note, Secret Life of a Party Girl, IS NOT Get Me Out of Here, it was recorded with Giles Martin, so it can't be)
Hopefully, sometime in the future, we'll see this song, for now though, it looks likes it's lost. If anyone has any more information, I'd love to hear! I can't even find the Japanese Import he's referring to, I'd guess it was on Amazon UK, but it's surely removed now.
Update: getback69 has informed me that the song was about Whitney Houston, and Paul decided to can the song because of her death. Seeing as she died only a month after the song was recorded on Jan 2012, and the first we heard of the song was over a year later, I would say it appearing in track listing was always a mistake.