URGENT HELP - Tier 2 ICT to Skilled Visa query

Hi,

I am currently in Tier 2 ICT visa valid until the end of 2022. In the meantime, I have got a new offer from different employer with skilled visa sponsorship with proposed start date as 24th June. The new employer have processed the skilled visa and I have received the skilled visa BRP in hand on 30th June with start date as 24th June 2021 valid until Dec'24.
Currently the Pre employment screening for new job is taking time and the employer have strictly advised not to inform my current employer until the PES is completed. The new employer have also confirmed that they will change the COS date to start of 1st September.
Currently my notice period is 1 month with my current employer, I am planning to resign by end of this month.

I would like to know will there be any problem working for my current employer until the end of August since as soon as I received my skilled visa my Tier 2 ICT would have been cancelled.

Your help and guidance on this is much appreciated.
guidance

Hi,

To add to the above question I was checking about the extension of COS start date and I found that the maximum the COS can be extended is by 28 days and not beyond that. In my scenario, the given COS start date is 24th June and the employer said they will change the start date to 1st Sep. Is that possible considering 28 days extension period or will they have to apply for new COS and new BRP again?

Thank You.