No, just one bill as normal. Your billing date won't change but next months will be higher and include your upgrade.
I have no affiliation whatsoever with O2 or any subsidiary companies. Comments posted are entirely of my own opinion.
This is not Customer Service so we are unable to help with account specific issues.Currently using:
Pixel 7a (O2 & Lyca), One Plus 6 (Sfr), iPhone 12 Pro Max (Vodafone)