End date and start date confusion

Hello

Greetings.

I have a UKVACS appointment for fingerprint on 15th April 2021. I am told that I have a priority service and the results would be known in 24-48 hours. The joining date at company Y is May 24 2021.

So, should I ask my current employer X to terminate my current CoS on 23rd May 2021 ?

Can somone guide me about how to plan the end date at company X and start date at company Y so that I will have continuity in my stay in UK for my ILR ?

Regards
Pranam

If you get the new permission (visa) you are only allowed to work for your present sponsor until the work start date in the new job.

Check your employment contract for the notice you are supposed to give to your present employer but this is not an immigration issue. Don't give notice until your new visa is confirmed.

There is no issue concerning continuity of residence.

Thank you.