I can't see a question in your post, so I'm assuming you're asking if they can be required to remove the termite nest?
The answer is 'probably not'. It will come down to where the property is. In most cases there's nothing you can do to compel a neighbour to do anything about a termite nest on their property.
However, there may be local council laws in your area that change that. I'm only aware of one council (Logan City Council) that has done so - their Local Law No. 10 has a requirement not to do/omit to do any act which causes a nuisance - and that includes having a 'wasp nest, bee hive or other insect nest on the premises .... is likely in the authorised person's opinion to give rise to a risk of ... property damage'. Premises is defined to include land, and termites are insects. So, if you're in Logan City or your local Council has a similar law, you may be able to complaint to the Council and they can require the termite nest's removal.
