Advice regarding tier 2 general visa (new employer)

[lille]

Hi,
I currently work for an employer on Tier 2 General Visa category and my contract end date is 30th Sept, 2019.
The current leave to remain in the UK is till 14th Oct, 2019 as mentioned on my BRP.
If I apply for another visa to work with a different employer (making sure that I meet all the requirements
necessary for that role),should the start date be earlier than /equal to my current leave (14th oct 2019)
mentioned on the BRP? Will I be allowed to stay in the UK if the COS start date is after 14th oct 2019?

Thank you.

[CR001]

You just apply, ie submit and pay, online for a new tier 2 BEFORE your visa expires.

Preaumably the full and proper RLMT has been done for 28 days if non shortage??

[lille]

Thanks for the reply. Also, how much time it usually takes for a sponsor to issue CoS?

[CR001]

Depends if they have completed rlmt before offering you the job and if they cos available to allocate to you.