As of now govt  issues NOC to an employee 3 times in a year.  They can not deny to issue NOC. 

Demand for NOC by written communication with a copy to the appointing authority and also to concerned ministry. You can issue the notice by any lawyer also but it is not essential.

In default file suit in appropriate court tribunal seeking directions to your employer to issue NOC. 

It is your right to apply for new job. Govt or other authority can not take away such right from you except in accordance with law. 

During probation period generally NOC is not issued 

you can submit your resignation and serve the notice period of one month 

You are under Probation, what is the need of NOC, ask him to give in written that probationer dose not require NOC.

Whereas general rule is Govt companies ask for application for NOC for appearing tests/interviews, and issue NOC mentioning that employee will be released after being selected. 

Dear Sir,

Yes NOC is issued during Probation period also. Send a request to the University  Head. . NOC is necessary if they have specifically asked for it. Normally you need to submit NOC only while attending the interview after clearing the written exam.

Normally Govt companies ask for application for NOC for appearing tests/interviews, and issue NOC mentioning that employee will be released after being selected. After being selected employee should give resignation with 3 months notice period or pay in lieu. In your case it seems your company is not employee-friendly (as you stated that they didn't give reply). Probably some experts give legal perspective for getting released from your company, if they are stubborn enough not to accept your resignation and release you. 

You can send him legal notice and then file a complaint with office of labour commissioner

- As per law, your current employer is bound to issue NOC for the Probation period ,  because NOC is issued during Probation period also.

- It is possible that NABARD ask for NOC from the last employer, hence it will be necessary for you to submit the same.

- Send your request to the HRM Setion of your last employer after submitting that for joining the othe employer , NOC required.

- If, no response, then you should issue a legal notice to them for the issue of NOC.

Probationer does not need to go through notice period as he is not a confirmed employee. You can give resignation letter and leave outrightly if you are a probationer.

Yes there is rule that an employee is not considered for NOC during probation.

And you don't even need NOC during probation period you can give resignation if you get selected for post in NABARD.

See since it is University and it is autonomous body it's rules have to be referred on your appointment if there are no such rules and regulation then you should be given NOCnotherwise NOC can be rejected.

Dont worry about the NOC, you may first apply for the post which you are aspiring now.

In case there is a necessity to produce NOC you may attach the written reply by the authority who denied to give NOC for the said reason.

The authorities cannot stop you from getting an employment outside their organisation for any reason, you have all the rights to be employed ion a better place however you may be required to comply with certain formalities.