The Reverse Charge is a mechanism for dealing with VAT where it becomes the customer's responsibility to account for VAT by showing it as both input and output tax on the VAT Return. The Reverse Charge is currently used in two specific areas - construction and electronic applications, e.g. Zoom or Dropbox.
The Reverse Charge only applies to councils that are VAT registered because of the way in which it is dealt with, i.e. recording it on the VAT Return. Therefore, councils that are not VAT registered (and just claim back VAT using Form 126) will not see this VAT type available in their account and nor do they need to record the reverse charge VAT element.
If you receive an invoice that states the VAT is subject to the Reverse Charge and your council is VAT registered (i.e. the VAT Registered box is ticked under Account/Council Profile) you will need to select this when adding the payment entry: