Tier 2 ICT cancellation doubt

[Genuineguy23]

I am on Tier 2 ICT visa (Long Term). My visa is about to expire in Dec 2017 (3 year period).
I plan to resign from my company.
I have got a job in Irelanland.
My initial plan was to join the firm in Ireland on March 1st.
But my new firm insists that I join earlier.
I am not able to leave UK earlier than March 1 due to some commitments.
Is it possible to cease work from my current employer in UK from Feb 21 and accept employment till end of February under the new employee? I read the grace period is 60 days.
So for the period between Feb 21 2017 and Feb 28 2017 is it possible to work in UK for the Irish employee , not having any payroll here but just working for the namesake?

[CR001]

You cannot work for another company, even remotely, except the one that is sponsoring the ICT visa.

[Genuineguy23]

Thank you