Applying for other Govt Job when your current employer is not providing NOC to you

No. You can't get NOC from the employer till you complete three years. When you are applying for any other government jobs you should give correct information and you should not hide the facts. They may create problems afterwards and it may even lead to termination from services. I know a person who joined in government service by giving wrong information. Afterwards he was terminated and disqualified from applying to other government jobs.
So it is better to wait for completing the said period and ask for NOC.
Some government jobs will be there which you can apply directly. As already you have completed 2 years and 2 months, you can apply for such jobs and the entire process may take more than 10 months and by the time you get the appointment you will complete 3 years of service in the present organisation and there will not be any objection for them to relieve.
If you want to go for a private job you can directly apply without NOC. But you should resign here join there.
It is always better not to take unnecessary risks. A bird in the hand worth two in the bush.

Yes, you can apply for the government job intimating the future employer of your exact status of the present employment. Since you have already completed 2 years 2 months in the present job and the condition is that you need to have completed 3 years of service for getting your NOC.
The processing of applications takes time such as sorting out applications, checking the eligibility status with respect to age, qualification etc and such process may range from 9 months to 1 year. Simply in your application, you have to state the details of your employment and your present experience and also state that NOC would be provided after completion of the specified period. Such request is always entertainable. Suppressing the facts would lead to your disqualification at the later stage if your case is exposed. Hence it is better to follow the existing rules of service.
In case, you are interested for a private job, you can resign from the present job and can join the new one. However, you will have to pay some additional money for your non completion of the minimum probation probation period if you have furnished a bond to serve the the government without any breach in the service.

As the job conditions say that you cannot apply or get NOC before three years, the employer is within his right to deny you NOC.
So the only alternative to you is to resign and get relieving certificate to be produced for the new job.
But you can still apply for any new job. In the application you should specifically note that you are under service with so and so department/organisation and that you will not get NOC now. So you should mention that if selected for new job you will resign the your current job and so need joining time sufficiency for the notice period and relief.

Now you have completed 2 years and 2 months. So unless extended, your probation period is over. You have thus a residual period of about 10 months or say less than one year to complete the service contract condition. As most general mass recruitment jobs take that much period for the procedures of recruitment you can be comfortably relieved /NOC obtained by the time you get a new job in govt/public sector.

For other jobs of low waiting periods, you can apprise the prospective employer about the facts and get the appointment letter permitting you to join after proper resignation and relief .
If you are to resign and join new job, please ensure that you are getting a written commitment as noted in above line.

You have accepted the terms and conditions of the present job while joining it and now there cannot be a deviation from that. If you want to apply for another Govt job then it will require NOC from the present office which you can not get at the present juncture as you have only completed 2 years and 2 moths time here. So the normal course of action will be to wait till you complete 3 ears and then only ask for NOC or apply to another Govt department through proper channel.

What is that other Govt department where you want to apply now. Is it in the same line or different? What is the difference of levels between that service and present one? These things are to be considered before you think to apply for a special permission or relaxation in this regard. Sometimes if the departments are linked and there is an urgent demand one can get opportunity for going there on deputation and in many cases one can get absorbed there. So you can consider this aspect also whether it is possible in your case or not. In case there is such a feasibility then you will have to talk to your superiors as well as in the concerned administrative section in your office regarding those modalities.

If you are applying for a private job then there is no requirement of NOC type of thing by them and you can comfortably apply without bothering for that factor. Still there will be issues like resigning instantly or with notice period and you have to take care in that and check with the terms and conditions of the present employment as what are the formalities to be adhered at the time of resigning. Sometimes if you resign with immediate notice (in your case before 3 years) you might have to deposit some bond money or one month salary as the case might be. So considering all these factors you have to take a conscious decision.

I feel that you are already working as a government employee and bounded by the service rules. It is not fair enough to leave the present job even though it may be a financial loss. You can always try another government job once the working condition period is over. When getting a government job has become so challenging factor for many, you want to leave the present government job and seeking another one which may not materialize. So better to continue the present job for another 10 months and then seek the NOC. By that time you may be an accomplished employee here in the first job and won't be parting.

As a Government officer with work experience of Establishment matters for more than 21 years, I have to state that in Government there is no rule that a probationer can't apply for other jobs for three years. This is not the rule and it can't be written in the service condition. Are you a Government employee or are you working in a PSU? Did you undergo training with a salary and sign a bond? Please clarify these points.

If you are a Central Govt. employee, these conditions are totally illegal and can't be included in the offer of appointment. You can challenge these conditions. If you have signed a bond after undergoing paid training, the bond can be transferred if you join a new Govt. organization. The rule position is very clear and in my own case, the bond was transferred.

Please clarify in which organization you are working at present and under which conduct rule you are presently being governed. Only then I can give you further advice.

PGIMER CHANDIGARH

So, that's the reason! My dear friend, Post-Graduate Institute of Medical Education & Research, Chandigarh, is not a Central Government Office. It is an autonomous body (like Universities and other educational institutions like IITs) which only follow the pay-scale of the Government. It has its own conduct rules. Further, most probably you signed a bond and as this is an autonomous body, there is no provision of transferring the bond.

Sir no bond signed by me.
It's a rule in appointment letter.

I understood that your office is not a Govt. organization when I read that the probation period is of 3 years because in Government, the probation is for two years. However, as you have not signed any bond, there is not much problem. You can apply for the new post without NOC, and if selected, you can resign your present position at PGIMER, Chandigarh.