I work as a benefits specialist within the NHS.
While there is no upper age limit for claiming Carer's Allowance, you cannot receive the full amount of both Carer's Allowance and your State Pension at the same time. This is because Carer's Allowance and State Pensions are classed as 'overlapping benefits'. However, you might still be able to get some extra money in recognition of your caring role.
If your State Pension is less than Carer's Allowance (less than £62.70 per week) you can get the difference paid in Carer's Allowance. For example, if your State Pension is £50 per week you can get £12.70 per week in Carer's Allowance.
If your State Pension is more than Carer's Allowance (more than £62.70 per week) you cannot be paid any Carer's Allowance. However it might still be worth claiming, as you can still get an 'underlying entitlement' to Carer's Allowance. Whilst this is not financially beneficial itself, it can increase any means-tested benefits you are currently getting or mean you become entitled to means-tested benefits for the first time (depending on your and any partner's income and capital). This is because having the 'underlying entitlement' to Carer's Allowance means that a Carer Addition will be included when working out whether you are entitled to means-tested benefits.
I hope this helps.