Timing of BRP (No Time Limit) application- before or after I got a new passport?

[chiho]

I got ILR in 2010. At that time, I didn't need BRP (Biometric Resident Permit)and have the ILR vignette sticker in my current passport. My current passport will expire in 7 month time (April 2018) and I'm planning to apply for a new passport in advance. My question is when should I apply for the BRP(No Time Limit)? As I don't want any disruption for work, should I apply for the BRP by premium service (with current passport) then I should apply for the new passport? (Is it possible?) Or should I apply for the BRP by premium service after I got a new passport?. As I heard it takes around 6 months to get BRP (postal application), I'm planning to apply it by premium service.
I look forward to hearing from your advice soon!