I have been work for an Indian organisation as a developer for more than 5 years. Let's call it XYZ. XYZ has a client called ABC. On the payroll of XYZ, I have been working for ABC. I didn't find myself growing here so I decided to find new employment. I got a call from an organisation based in UK (let's call it MNO). Gave the interviews and was hired.
I gave my resignation to XYZ last week, telling them that my last working day is 10th May, 2024. To MNO, I have let them know I am joining by 20th May, 2024. MNO accepted the date, gave me an offer letter, which I have signed.
XYZ also accepted my resignation but they didn't accept my last working date. They are saying they need to talk with ABC, the client, in order to work on when they can relieve me and it also depends on how quickly they can hire someone new to train them on the work I have been doing. They are also taking too long to initiate a conversation with ABC despite me reminding them almost everyday.
What are the options I have at hand? How do get myself relieved earlier? Are there any solutions I can suggest to my current employer?
EDIT: My notice period is 90 days according to the policies. But I have requested an early release. There is an option to buy out the amount of notice not served but the company reserves the right to accept the buy out option or not.