Quitting a New Project?

I am working as a fed contractor. I have done this on and off for over a decade and genuinely enjoy the experience. Last year I got a new exciting contract, but the lead on the project had issues with me for some reason. Earlier in the year the company I contact to had a meeting with me about those issues They said all was fine, but wanted my perspective on things which I gave them. I didn't exactly believe them though so I started looking for another job immediately. Fast forward one month and they no longer hold this contract and I am off of it They found a new position for me which I was obviously grateful for and stopped looking. Then I get a call about another contract that I interviewed for. It pays more and moves me into a leadership role which is something I have wanted for a long time, so I accepted it. I will have to give notice soon, but am nervous about being walked off the day of since I just started this project and am barely done onboarding. If I was still in my old role this wouldn't be an issue Any suggestions on how to handle this?