It is NOT possible to delete a staff account in HappyFox.
As an alternative, you can disable a particular staff through "Manage" >> "Staff" >> 'Uncheck' respective staff.
Clicking on the checkbox will open a popup where you can choose to assign the respective staff's pending tickets. or all the tickets to someone else, or leave it unassigned. Once done, click on "Update" button.
This will unassign all the tickets that were assigned to him/her in the past.
Note: Once you deactivate a staff account, the staff will not have access to the HappyFox account.
Also, the deactivated staff accounts are not considered in your 'Billing cycle' when calculating the total staff license limit. So, you can go ahead and create a new staff, as and when required.