Yes, having a private pension doesn’t stop you receiving any state pension you are eligible for.
It doesn’t matter how many other pensions you have paid into over your career, as long as you have made the relevant National Insurance contributions for 30 years you will be eligible for the full state pension. If you have 10 years or more of relevant contributions, you will receive a partial state pension.
Brookson Advice:
You can check your state pension status including how much it is currently worth and when you can begin taking it at gov.uk/check-state-pension