NOC for DV and joining in bank

You don't require any NO Objection Certificate. When you have applied for IBPS RRB PO examination. You have informed about this RRB PO examination also. Once you get selected for the post, you can resign for the present post and get the relieving letter. Once you have the relieving letter you will not have any problem. Nobody will ask you NOC.

If you have to send the application through proper channel or you have to get the NOC only when you apply for the post while you are in a job.

At the time of applying for banking services you were not employed so there was no question of applying under a NOC mode. Your joining in the central Govt department is a subsequent event. So you do not require to produce a NOC from the present department for your document verification process or joining in the banking services. So do not worry in that matter.

One thing which is important at this juncture is your terms and conditions in the present employment. How much advance you have to tender your resignation here and if you want to immediately leave the present organisation what are the modalities involved - whether you have to deposit or forgo one month salary in lieu of the one month notice period - these things you can get clarified from your present office so that you can move ahead smoothly from the present job to the anticipated bank job.

As per your query and my understanding,
i) You have joined the central govt. department on 11-11-2019 and accordingly, you will be completing your 3 months probation period tomorrow. I would request you to provide your resignation letter through proper channel to the department. As you have not completed your probation period, it will not be a tuff task for the department to relieve you and even accept your resignation.

ii) You had applied for IBPS RRB PO on 25-06-2019 that was much before joining the central govt. department and thus they should not have any objection in accepting your resignation and relieving you of your current designation with a short period of time or as per the rules and guidelines of the department. You can approach your HOD or HR and inform them about the present situation and your reason for the resignation, they will be able to relieve you at the earliest as you are still under probation.

In the meantime, you can accept your appointment letter and seek time if possible to get your resignation approval from the central govt. department so as not to be a hindrance in the future.

Since you had applied for IBPS RRB PO on 25 - 6 - 19 when you were still looking for a job and your absorption in the central government was effected on 11- 11- 19, hence under such a situation, you need not worry regarding the NOC submission to IBPS.
However, you have taken a best recourse by intimating your present employer regarding your selection status in the IBPS.
Once you get the appointment letter of IBPS, please go through it where in you would get the date of your joining failing which your candidature for the post would be cancelled. However, you can take extension for a minimum two months with the appraisal of the situation to your next employer and asking the next employer for an extension to the extent of the period when you could be relieved completing all the necessary formalities of relieving of your present assignment. However, in such a case, your seniority in the IBPS would be affected to some extent. This might affect your promotional status in the later stages in IBPS.
Hence ensure that you are relieved timely so that your seniority in the next post is not affected.