When you die, your ISA becomes a 'continuing ISA'. This means it can remain open for up to three years and one day from the date of death. This ensures time for either the administration of your estate to be completed, or for the ISA to be closed by your executor. If neither happens within the timeframe, the ISA provider will close it.
Before the ISA is closed, it will continue to grow and keep the tax benefits that an ISA brings. Although additional funds cannot be added to the ISA, further growth or returns will not be subject to income tax and capital gains tax.
However, ISAs form part of your estate, so they are subject to inheritance tax. If your estate is worth more than the current inheritance tax limit of £325,000 and you leave your ISA to anyone other than your spouse or civil partner, they'll pay inheritance tax. (Spouses or civil partners are not required to pay inheritance tax.)
In addition, your spouse or civil partner will inherit a one-off additional ISA allowance known as the 'Additional Permitted Subscription' (APS). This allowance is equal to the value of your ISA at the date of death or when it's closed (whichever is higher), but it will not affect your spouse or civil partner's own ISA allowance.
APS means that if, for example, you left an ISA worth £65,000, your partner would have an additional permitted subscription of £65,000. This additional ISA allowance can be used even if the money is left for someone else to inherit, such as a relative who isn't your spouse or civil partner.