UK immigration law is aligned with C.I. immigration law but they are not the same, for example I believe the C.I. don't issue BRPs to skilled worker visa holders. However, applying for a BRP is a requirement for getting permission for your new job in the UK. I also understand that there are no UKVCAS centres in the C.I. where your biometric data could be captured but one way to overcome this may be to use the "UK Immigration: ID Check’ app to complete the identity verification stage of your application:
https://www.gov.uk/guidance/using-the-u ... -check-app
https://www.gov.uk/guidance/using-the-u ... se-the-app
Although there doesn't seem to be clear guidance on the gov.uk website covering your situation I suggest you try using the change of employment (in-country) application form and to get on answer Yes to the question whether you are located in the UK. Also if they ask for your BRP try entering the C.I. vignette No from your passport.
Please let the forum know how you are getting on with the application.
