The processing needs to be done by your new employer. Follow up wit them for the status of your transfer. It takes a week to 10 days. By the way check with your new employer if they will also bear the expenses of renewing the RP incase it expires before the said transfer process is done. If yes, then you don't have to worry about anything and just follow up with the new employer. Your work is almost done but your new employer needs to do 100% of more work.

Regards,
SM