Incomplete years due to severe mental health problems (subequently awarded ESA)

From 2009 to 2013 I was very ill to the point where I could rarely leave the house; hence not being able to secure evidence for an ESA claim. I instead claimed JSA but had to sign off frequently as I was unable to attend appointments. After getting slightly better and with support from a relative I was able to claim ESA (awarded on appeal, took over a year). However I have been left with 4 incomplete years for NSI contributions. It may be inconsequential but I'd rather not have to worry about it (no-one can guarantee that the 35 years for a full pension won't increase to 40 for example). Should I write to the individuals caseworker with supporting evidence or is there a different avenue for cases like mine?

Hi ep1987. 
Guidance in relation to paying previous years National Insurance Contributions is covered at: Voluntary National Insurance: How and when to pay
As you can see the deadline for making payments to cover gaps from 2006 to 2018 is 05 April 2025.
If you have any doubts or supporting evidence then please use the contact options including post as shown at: National Insurance: general enquiries
To ensure that the deadline for previous years is met you must complete the 
call back request form by the 05 April 2025. 
This is also  available at Contact the Future Pension Centre 
You can then check the allocation of national insurance payments and full years through the following if you have set up either: 
• your personal tax account 
• the official HMRC app
Alternatively you can Check your National Insurance record through the links available.
HMRC nor DWP staff can only advise on the qualifying rules for state pension on the date you contact us.
We are not party to any future changes that might be advised by The Chancellor of the Exchequer.
Thank you.