Having paid into a db pension, it is almost certain that it was contracted out of the State scheme, so the years paying into the db scheme won’t count towards your required 35 years to achieve a full State pension.
See this link to money saving expert on the subject of State pensions for more info.
https://www.moneysavingexpert.com/savings/state-pensions/
You can buy up to 10 years of contributions to make up your State pension, which can work out as a very good investment with payback in as short as 3 years. I suggest you talk about this option with your financial advisor.