for case transfer in fast track court

File an application before the Court for early hearing of the case, justifying your concern.

However, you may move a petition to High Court under Article 227 of the Constitution of India through your counsel for issuance of necessary direction(s) to concerned subordinate court to finalise the matter within a time frame,

it cannot be automatically transferred to fast track court or by filing a petition to transfer the same to some other court without any proper reason, that too it shall be decided by the high court only.

The delay in civil court is known fact hence you may not be able to push it by such applicaitons or petitions, you may introspect the reasons for the inordinate delay, if the delay is due to unavoidable reasons, then you may not be able to push them forward

It is a civil case.

Is there any provision / rule for establishment of "Fast Track Court" for adjudication of such (civil) suits / cases in any of the State(s) in India, which I am not aware ?

If a civil case has been stalled for more than four years, it can be transferred to a fast track court under *Section 526 of the Criminal Procedure Code* ¹. This section grants the High Court the authority to transfer any case from one court to another, including to a fast track court. However, the application to transfer the case must be made by the party seeking transfer and must be supported by sufficient reasons and grounds for such transfer. Additionally, the court may also take into account factors like the age of the case, the complexity of the issues involved, and the interests of justice.