Will there be any objection in our car loan if we have been paying our plan for 3 years now?

You need to get trustees permission.

Whether there will be an objection will depend on the terms of the new proposed vehicle loan. After all, the trustee will still want you to be able to afford the payments provided in your current confirmed Plan.

I gather from this question that what you are saying is that you are in a 5 year Chapter 13 plan, so that in the third year now you are not yet near the finish line. Your vehicle is quite old with significant mechanical problems and it is not financially prudent to repair it and therefore you wish to purchase a replacement vehicle, which you hope to finance. You also understand that in order to take on new debt(s) while in a chapter 13, such debt(s) must first be approved by the court. You will need to file a motion to get permission prior to financing. As long as the replacement vehicle you are considering is reasonably priced and a dependable vehicle is necessary for you to get to and from work, such motions are generally approved. To be certain as to the answer to this question you'll have to file your motion.

You or your attorney will need to contact the Chapter 13 administrating your case to find out the requirements that the trustee has for this proposed transaction. You will need the trustee's consent.

Ask your bankruptcy attorney. Changing anything inside a chapter 13 is complicated.

It should be fine, but you should contact your attorney for assistance and to make sure that proper procedures are followed. Depending upon how your current car was treated in your plan there could be a need for modifications.