The new nest was found by the National Bee Unit in New Alresford, Hampshire, following a report from a member of the general public.
The nest was promptly destroyed by the APHA Wildlife Team and the bee unit is continuing to search for further nests, with support from local beekeepers.
There have also been confirmed cases in Hull and Cornwall.
Two nests have now been destroyed in Cornwall and surveillance in this area continues.
No live hornets have been seen in Hull since a single dead Asian Hornet was found in a house, despite extensive surveillance.
The appeal says: “The New Alresford response highlights the importance of public awareness of this species and we are encouraging all stakeholders, particularly in the Cornwall and Hampshire regions, to help raise awareness of the need to be vigilant and report this species.”