Is it necessary to apply through proper channel for another job in Govt or PSU??

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.

If you are an employee of a public undertaking and are interested for a post existing in another public undertaking, there are two ways of approach. Firstly you will have to apply through proper channel where your application will move through the different channels of your present organisation. Your immediate boss would forward a note- sheet along with your application. The boss would forward the same to his higher ups with the remarks of no objection and there will be even the concurrence of this from the higher ups and the officials of the personnel department and finally it would reach to the organisation where you are interested to join.
In the event of your selection, you would not face any dislocation due to compliance of the standing order.
The other option would be to secure a NOC along with your application to the next employer so that the next employer would not face any problem in case you are found fit in the selection process.
Relating to your query that you have cleared the written test of a PSU and you did not convey the same to your present employer. It would be treated as a kind of indiscipline. Have a talk with your immediate boss and the personnel department and in that way, you can manage your NOC.
Without your NOC, you would not absorbed in another PSU unless you resign from the present post. However doing so, you would loose your seniority and there will be your break of service causing severe loss in terms of your PF and gratuity which you would have enjoyed a higher amount than the existing one.

When you are working in a PSU or Govt organisation then you are bound to it as per the terms and conditions of your employment and you have to take any action for applying to outside organisation as per the procedure. One has to apply for outside organisations through proper channel and one can send the advance application directly also so that one can appear in written test and interview. Meanwhile NOC from your current organisation would be given to you and that you can produce to the new employer.
There are certain things in this matter which are important to be noted. First is sometimes the current organisation might delay the issue of the NOC and one has to pursue it may be even at a higher level. Another thing is that when you resign then you have to give a notice of a few months as per the procedure in your organisation and if you cannot give a notice for the stipulated period then you will have to shell out the salary for those months means you will not get that salary. Then, if you have executed some bond then you would have to honour that bond, if you are leaving the organisation within the time limit of that bond. Your organisation must have spent on your training etc and now if you are going to leave they will realise the bond if it is applicable as bond has some period of validity.
Nowadays provident fund and other such matters are under online control and that would also be required to be linked when you move from one organisation to other.
If you apply in other organisation without telling to your current organisation then the new organisation would treat you as a fresher as they do not know about your employment elsewhere. In that case you would need not to produce a NOC as you have presented yourselves as unemployed. Then you have to see how you will manage leave for written exam and interview and then when you suddenly leave your present organisation, you will have to deposit the salary against the notice period and honour the bond, if any such bond is there. In such a case you cannot take any advantage of your experience in the current PSU also as you have hidden that fact and your new organisation will take it seriously as hiding of personal information. Your present tenure will become a black box.
So there are many aspects and fine points in this and you have to understand the implications of all these to take a decision for this NOC issue.

Is it necessary to apply through proper channel for another job in Govt or PSU??

It is not necessary or mandatory to apply through proper channel, you can approach to your Employer to provide a no objection certificate for appearing the proposed interview. If they issued it then your certain benefits like experience, Pensionable service etc will continue otherwise you have to resigned from your existing employer if you are selected with new jobs. thanks