When you are working in a PSU and if you want to apply for another position in another PSU, you have to follow the instructions, terms and conditions of your appointment. You have to follow them without fail. Again the advertisement against which you are applying will also mention the way you have to apply for those posts. Those points are to be followed.
It is always the best way to apply through proper channel. Once your present employer forwards your application, you can take it that there is no objection for the present employer. In such a case, you need not get NOC from the present employer. If you are not applying through proper channel, you should get a NOC from the present employer. Some PSUs don't allow for the written teat and/or interview without NOC. Some may allow but may not select you in case you are not submitting your NOC during document verification or interview.
If the present company is not giving you NOC, you may have to resign the present post and get the relieving certificate from the present employer and then join the new employer. But there will not be continuity of service and you may lose your seniority also. So it is always advisable to have a NOC from the present employer when you go to a new PSU.
I advise you to apply for NOC and attend the interview with your NOC only if you have not applied through proper channel. Generally, no PSU will select a candidate who is working in another PSU and attends the interview without NOC.