If you're married or in a civil partnership, if your partner dies you can inherit a one-off extra ISA allowance on top of the annual £20,000, up to the total amount they had saved in ISAs. These are known as 'additional permitted subscriptions' (APS).
You have a few choices. You can simply keep the ISA with the same provider, move it to a different provider that accepts APS (not all do), or the ISA goes to someone else but you get the extra allowance. To claim your allowance, you'll need to give your partner's full name, address, date of birth and date of death, your marriage/civil partnership certificate and their national insurance number if you know it. Some providers may also require a copy of their death certificate.
The allowance you'll inherit will depend on when your partner died:
Before 6 April 2018. You'll inherit an allowance equivalent to the total value of your partner's ISAs at the date of death.
On or after 6 April 2018. You'll inherit an allowance equivalent to the total value of the ISAs once their estate is settled, when their ISAs are closed, or at the third anniversary of their death, whichever is earliest – so any growth in value will be taken into account.
The inherited allowance is available to make use of for three years after your partner has passed away, or 180 days after the completion of their estate, whichever is later.
Note that inheriting the allowance is not the same as inheriting the cash in the ISA – your partner could, for example, leave some or all of their ISA money to someone else. You'd still get the extra allowance but would have to fund it with your own savings.
If you're not married or in a civil partnership you won't inherit any extra allowance.