Resident labour market test exemption for tier 2 visa holder

I am presently sponsored by my current employer under the tier 2 general visa but my employer didn't go through a resident labour market test to hire
me because I had tier 1 post study work visa as at time of application.

I would like to find out if a new employer is exempted from the test if I decide to switch job to the new employer now.

Regards,

Any future new employers have to complete the RLMT unless it is a shortage occupation.