I handed in my resignation on August 18 with a 3-month notice period, making my last day November 18. However, my new employer wants me to start on November 16. I reached out to my current manager, who confirmed he had no issue shortening my notice. Despite this, my current company has been slow in finding my replacement, and they haven't conducted any interviews yet. My new manager has been checking in on my negotiation progress, and while they are flexible, I have a pressing reason to start earlier. The person who took the Lead position I originally interviewed for has sadly passed away, and my new manager wants me to join ASAP to evaluate my performance for that role. I have 8.5 days of annual leave left, which I plan to use to potentially move my last working day to November 6. HR mentioned they could require me to work until November 18 and pay out my holiday, but I pushed for an earlier termination date. I suggested October 30, and my manager said he would discuss it with HR, but I haven't heard back yet. I want to avoid burning bridges since I'm moving to another contractor on the same site, and my current employer needs to process my departure for the onboarding with the new company. Ideally, I want to secure an October 30 release, but if that doesn't happen, I'll stick with the previously agreed November 13 date. I'm looking for advice on how to navigate this situation without damaging my relationship with my current employer.