More information: Currently on a UK Tier 2 sponsored visa that is being sponsored by my current employer. I just got an offer from another company that is willing to sponsor my Tier 2 visa. I will like to know if the UKBA will notify my current sponsor if I try applying for a new Tier 2 visa using the new Certificate of Sponsorship that the new company will issue to me.
The current employer will not be notified. The caseworker will check BOTH employers in the SMS. If your T2 is an ICT, you will not get a relaxation on any applicable cooling-off periods.
People use a new CoS to change jobs all the time, there is nothing particularly unusual about it.