As per the official notification CSIR NET June 2020 will be held on 21st June 2020. Till now there is no information related to delay of exam.
As there is only one month left to prepare for exam, you have to boost your preparation and revise all topics whatever you have studied till now.
Solving CSIR NET Previous Papers and mock test will be the best strategy for you to prepare in last one month before the exam. Through this, you can boost up your confidence level and you can analyze your performance as well.
I’ve mentioned a link above where you can find all these question papers.
Hope you will get best out of it.
All the Best!!