Does obtaining CSI now make up for CSI absence in the past?

No, obtaining CSI in the present won’t make up for the lack of CSI in the past. You would need to have had CSI during your past time as a self-sufficient person or as a student in the UK. 

It is better to wait until the gaps no longer form part of your 10 years before applying for citizenship, or apply before that time and ask for discretion.

Note: this question, like other FAQs on Comprehensive Sickness Insurance (CSI), relates to applications for British citizenship, when considering whether periods of past residence were lawful.

CSI was not required to apply for pre-settled or settled status under the EU Settlement Scheme. Also, once pre-settled or settled status is granted, you are lawfully resident, and you do not need CSI.