You cannot inherit someone else’s ISA when they die. However, you will inherit an extra ISA allowance based on how much was saved in their ISAs.
If your spouse dies (whether married or in a civil partnership), you will inherit their savings through what is known as an ‘additional permitted subscription’ (APS). This means the spouse will gain a one-off additional ISA allowance on top of their annual ISA allowance.
For example, if your spouse dies with £50,000 in their ISA, you will inherit a one-time £50,000 allowance top-up on your £20,000 ISA allowance limit but will be using their own money to do so.