@suvra jyoti Application Insights doesn’t support disaster recovery as of now. But please do note that Azure Monitor logs will soon be supporting availability zones and it doesn't require additional deployment as well.
Regarding to your question on how to set up high availability , you might have to create separate application insights for both the regions. Same question has been answered here.
I also would recommend you to navigate here and share your feedback or suggestions directly with the responsible Azure feature team and clicking the vote button of your suggestion to raise visibility and priority on it.
Reference video for high availability information: https://channel9.msdn.com/Shows/IT-Ops-Talk/OPS115-Log-Analytics-workspace-design-deep-dive