This is a follow-up to the article written last night, South Sudan Embassy Just Got A Bad Rep, A Really Bad Rep. Assault Story in New York. A Discussion About Diplomatic Immunity.
There are recourses for the administration of justice. Just what exactly they are on a practical level, may take a moment or two to collect.
Here are some basic guidelines:

1. First, document the incident the best possible.
2. Second, seek an immunity waiver. (If the suspect is invoking diplomatic immunity to protect himself from continually being in the state of being arrested, that immunity can be taken away by the country that sent him here.) To obtain the waiver, the State Department may have to request it.
3. If the waiver is denied, seek an expulsion of the referent diplomat. (Realize that repercussions may be dangerous to the suspect if he does get sent home, as in sent back to his home country or sending entity, and that it is diplomatic procedure for expulsion to occur in certain situations which are severe, cases less severe than this receives this treatment, and therefore, there might be a probability that the waiver will be granted, allowing the suspect applicable amount of flexibility after having no further immunity.)

What could happen, is an immunity waiver could be requested, if granted, suspect rearrested and, or a warrant for arrest or court appearance be issued, and he brought before US or local court such as the one attached to the police department which he was initially arrested, perhaps with some kind of monitoring given the diplomatic circumstance could occur, tried before such court, punitive actions established, the diplomat could then be terminated from his post, or in some order of that. Lawyers for all sides, prosecutors, NYPD, State Department, likely most of the pertinent parties involved, and swiftly reach a conclusion or best action.

The suspect can not and does not have to be considered let to continue on scot-free with no punitive repercussion.

Detailed notes:
There are some courses of actions that can be taken as set forth by the State Department, here are some excerpts with boldface to provide a general framework:
The term diplomatic immunity is popularly, and erroneously, understood to refer to special protections afforded all employees of foreign governments who are present in the United States as official representatives of their home governments. (Per State Department's Guide to Law Enforcement on Diplomatic and Consular Immunity, 2018).
It should be emphasized that even at its highest level, diplomatic immunity does not exempt diplomatic officers from the obligation of conforming with national and local laws and regulations. Diplomatic immunity is not intended to serve as a license for persons to flout the law and purposely avoid liability for their actions. The purpose of these privileges and immunities is not to benefit individuals but to ensure the efficient and effective performance of their official missions on behalf of their governments. This is a crucial point for law enforcement officers to understand in their dealings with foreign diplomatic and consular personnel. While police officers are obliged, under international customary and treaty law, to recognize the immunity of the envoy, they must not ignore or condone the commission of crimes. As is explained in greater detail below, adherence to police procedures in such cases is often essential in order for the United States to formulate appropriate measures through diplomatic channels to deal with such offenders.

Diplomatic agents enjoy the highest degree of privileges and immunities. They enjoy complete personal inviolability, which means that they may not be handcuffed (except in extraordinary circumstances), arrested, or detained; and neither their property (including vehicles) nor residences may be entered or searched. Diplomatic agents also enjoy complete immunity from the criminal jurisdiction of the host country’s courts and thus cannot be prosecuted no matter how serious the offense unless their immunity is waived by the sending state (see the following discussion).

Waivers
Always keep in mind that privileges and immunities are extended from one country to another in order to permit their respective representatives to perform their duties effectively; in a sense, it may be said the sending countries “own” these privileges and immunities. Therefore, while the individual enjoying such immunities may not waive them, the sending states can, and do. Police authorities should never address the alleged commission of a crime by a person enjoying full criminal immunity with the belief that there is no possibility that a prosecution could result. The U.S. Department of State requests waivers of immunity in every case where the prosecutor advises that, but for the immunity, charges would be pursued. In serious cases, if a waiver is refused, the offender will be expelled from the United States and the U.S. Department of State will request that a warrant be issued and appropriate entries to the National Crime Information Center (NCIC) database be made by the responsible jurisdiction. The seeking of waiver of immunity is handled entirely via diplomatic channels, but effective and informed police work becomes the basis of the prosecutor’s decision and the foundation for the U.S. Department of State’s waiver requests and any subsequent prosecutions or expulsions.
Correct Understanding of Immunity Frequently (and erroneously), immunity is understood to mean pardon, total exoneration, or total release from the responsibility to comply with the law. In actuality, immunity is simply a legal barrier which precludes U.S. courts from exercising jurisdiction over cases against persons who enjoy it and in no way releases such persons from the duty, embodied in international law, to respect the laws and regulations of the United States.

Waiver of Immunity Diplomatic and consular immunity are not intended to benefit the individual; they are intended to benefit the mission of the foreign government or international organization. Thus an individual does not “own” his or her immunity and it may be waived, in whole or in part, by the mission member’s government. The U.S. Department of State will request a waiver of immunity in every case in which the prosecutor advises that he or she would prosecute but for immunity. The U.S. Department of State’s ability to secure such waiver may depend to a large degree on the strength (and documentation) of the case at issue. Similarly, it is of little avail for the U.S. Department of State to secure a waiver of immunity in a particular case, if the case has not been developed with sufficient care and completeness to permit a successful subsequent prosecution. Proper documentation and reporting by law enforcement authorities play a critical role in both of these respects.

Expulsion Procedure
The criminal immunity that foreign diplomatic and some consular personnel enjoy protects them from the normal jurisdiction of the courts with respect to alleged criminal activity. However, in those instances in which a person with immunity is believed to have committed a serious offense (any felony or crime of violence) and the sending country has not acceded to the U.S. Department of State’s request for a waiver of immunity, it is the Department’s policy to require the departure of that individual from the United States. Requiring the departure of a person who enjoys immunity is an extreme diplomatic tool, and it is used only after the most careful consideration to ensure that the United States is not perceived as having acted in an arbitrary, capricious, or prejudiced manner. A high standard of police investigation, records, and reporting in diplomatic incident cases is therefore essential to permit the Department to make the appropriate decision.