Quitting IB job before PE

This has been covered before—but generally no. The expectation and the reason PE firms hire you is that you will have 2 years banking experience before starting. However, what you can do and is done a decent amount:

• Call the PE firm and let them know you would like to work for another firm in the industry, I.e. move to a growth equity or another PE firm for a year instead of your bank. You need to be clever and delicate about how you handle this, but you can just say you feel you aren’t growing much, the culture isn’t great, and think you’d be a better asset to the PE firm if you took a job at x. Usually you want to have the offer in hand before doing this. 
• If you are a 3rd year (you already have 2 years of banking experience) you can let them know you will be taking some time off before starting your role. This is viewed more favorably since you already did your time and they know you are getting marginal benefit from year 2 to year 3.
• The time matters, a 12 month gap is ridiculous. Also, I don’t know what you are doing for 12 months and it’s a bit of a red flag to future employers. Explaining that you “had an offer in hand” and just did squat for a year isn’t going to go well with any employer and anyone in the future will assume you are a clown. What is more sellable is a 3 month gap to travel, as mentioned exploring an alternate career path, or some sort of legitimate reason for taking a gap between roles (having a sick parent, being a Mormon missionary, etc.)