If the ASA is running in failover mode, I would organise for a maintenance window to perform license update as I have seen issue where it breaks the failover if the license is not updated at the same time. If you update the license on 1 ASA, and not on the other at the same time, the failover will detect that license is no longer synchronised between the 2 ASAs, and will disable the failover. I would stongly recommend maintenance window to add the license, and take the following steps:
1) Make sure that the license/activation key that you received is for the correct serial# of the ASA.
2) Prepare the "activation-key" command for both the primary and secondary ASA
3) Paste the activation-key command to both ASA, but don't press "Enter".
4) Press "Enter" on both ASA at the same time (one quickly after the other is OK).
Hope that helps.