Fred Astaire Fallaway and Rock was my guess too, although my interpretation of the figure is slightly different:
Steps 1-3 are very simply the first 3 steps of a closed bronze box, taking 1/4 turn to left to end with man backing diagonal wall. The way Sageon and nloftofan1 describe it, step 3 is already turned to fallaway position (feet nonetheless closed), but I feel it's stronger not to open up quite that early. It's also much easier to describe.
Steps 4-6 are a simple Slip Pivot, which in our syllabus is full silver step #41 in waltz (link here:
https://www.ballroomdancers.com/Dances/info.asp?sid=793).
Step 4 is not actually the slip pivot action itself; It is a step side & slightly back for both man and lady, turning to fallaway position (if they're not already in fallaway). 5-6 is the slip pivot, man LF back & across in fallaway, then RF slipping back in CBMP and pivoting to the left on the foot with LF held in CBMP. Lady meanwhile steps RF back & across in fallaway, slipping the LF forward in CBMP to transition back to closed position, and pivoting on the LF with RF held in CBMP. It ends with man facing LOD, the couple having turned a total of 5/8 over the 3 steps.
In our syllabus, the slip pivot consists of just those 3 steps, giving you some flexibility to mix and match whatever you like as precedes and follows. For example, you could precede with 1-3 of a Left Box Turn (bronze), 4-6 of a Right Box Turn, or a LF Side Hesitation or Side Whisk. You could follow with just about any reverse figure such as a Left Box, Left Cross Turn, etc, or a progressive figure such as a Closed Change, Passing Change, just about any kind of Twinkle, etc.
The old Fred Astaire pattern was, as nloftofan1 mentioned, followed by a Left-Turning Rock, a sort of undercooked Reverse Pivot taken to a straight count of 1,2,3, which leaves the man backing LOD with his RF free to finish a Box. One of our Waltz variations of the week (link here:
https://www.ballroomdancers.com/Dances/info.asp?sid=1060) is a spin-off of this figure, but instead of completing all 3 counts of the Left-Turning Rock, you dance 1-2, then the man turns away and finishes the third step in promenade position -- almost like an Open Telemark without the lady's heel turn. This variation is about as close to the full Fred Astaire pattern as you're going to see online. As you might imagine, we chose to wait until step 4 to turn to fallaway.
Regards,
Jonathan Atkinson
www.ballroomdancers.com