Is it advisable to get new insurance for two wheeler which is in another party's name.

You need to first transfer the bike in your name as you are an owner right now and then can go ahead to renew the insurance policy on your name, easily. But the case is little different and critical now. How? Since the insurance is already expired, you need to first renew it at the moment in previous owner's name in order to avoid the penalty upon cop catches you for various document including insurance.

If it is already renewed and it is valid in last owner's name then you could avoid penalty for a year at least time being and be safe.

In these time or within a year after renewal of the insurance to last owner's name, you can then transfer the bike to your name so that next year you can renew the insurance on your name, safely.

Insurance vehicle always have better value. So, it is always better to spend few hundred or thousands to keep all the required documents of the vehicle to avoid any mishap.

Third-party insurance is very important and if you don't have insurance, you will be asked to pay penalty and you will be at risk if you have any incident unwanted. So you can't avoid insurance.
The insurance papers will have the number of the vehicle and the owner of the vehicle. Now you can't get the insurance on your name as all the papers are in the name of the person who sold the vehicle to you. The letter he has given is not legally valid as that document is not a registered document and in case of an accident, this letter can't take away the responsibility of the other person as long as the papers are on his name. That is why many people for a change of name of the owner as soon as it was sold.
You have to take immediately insurance on the name of the previous owner only. If there is time you can change the papers of the scooter on your name and then you can take the policy on your name as the owner.

First and immediately take steps to transfer the ownership of the vehicle in your name and get it recorded in the RC book . Verify the RC book for any lien by any bank. If so that has to be settled first.
Immediately take insurance on the vehicle in your name. Avoid taking the vehicle without all these legal and absolutely necessary formalities.

You will have to take up the following points as mentioned below-
1) There is a big catch in fixing the issue since the term of insurance has already expired already done against the previous owner. In order to avoid any legal complication, there should be extension of the insurance policy in favour of the previous owner.
2) Once the bike is insured against the previous owner, get the vehicle transferred in your favour through the vechile registration department and even in the owner book of the vechile, your name has to be introduced.
3) Once the ownership is transferred in your name, get an insurance policy in favour of your name.
You need to examine all the relevant papers indicating the name of previous owner and then change of names is be taken up uniformly in all such papers such as Road - tax papers, Owner - book and Insurance - paper so as to safeguard yourself from the legal complications.

You have purchased an old bike from someone and based on a sale deed now this bike belongs to you. But in the RTO office it is still in the name of the earlier owner and the office does not know that the bike has been sold to someone. God forbid if an accident takes place with this bike then it would be difficult to explain to the police and other authorities about this delay in transferring the bike in the new owner's name as well as unavailability of insurance on the date of the accident.

Apart from that as per statutory regulations there should be at least a third party insurance if not the comprehensive one for all the bikes or vehicles in our country so that any unknown and innocent person who gets entangled in the accident can get the benefit of third party insurance. At this stage what I would suggest is to cancel the present sale deed and make a fresh sale deed only after the original owner renews the insurance in his name and gives a copy of that to you. After that date only a new sale agreement between the original owner and you is to be prepared signed by both the persons. Then, you apply for change of address and ownership for the said bike and once that is done on that basis there would be no difficulty in changing address in that renewed insurance policy. Please note that because there is some hassle in getting change of ownership in RTO office, we should not ignore the rules and regulations as not following them would land us in grave difficulties in case of some eventuality later.

Yes, every vehicle needs to get insurance for the same. Either the owner is you or any other party. The driver or owner must have the personal insurance of at least fifteen lakhs; which is mandatory.

If the vehicle is not in your name, then any claim will be settled with the owner (whose name is mentioned on the registration of the documents).

Well first of all do not know the exact reason why you not willing to transfer the vehicle on your name which is mandatory for any individual in terms of claiming insurance on his name. Second thing insurance of any vehicle will be done only on the name of the owner of the vehicle , if you are not owner then you cannot claim any insurance. So my best suggestion for you is transfer the vehicle on your name then you can pay the insurance on your name and so as can claim on your name only. If you renew the insurance on previous owner name on whose name the vehicle too registered only can claim for insurance . And whole rights of the vehicle too comes under his name.

Since the insurance has expired and you will be using this vehicle regularly. It is better to get the new insurance policy.

You can apply for the insurance of the bike in the first owner's name itself. There is no other option so it has to be followed. Once you have the insurance and the documents required for change of ownership, later you have to get the No objection certificate and apply to RTO for transfer of ownership.

After purchase of a bike from a person there are two things which are to be done immediately. First is to get the change in the name of the owner and address in the RC book or card of the vehicle from the transport office. Once that is done then that is to be produced to the insurance company for change of name and address in the insurance policy.

In this case the policy is already lapsed so first thing now is to renew it in the name of the earlier owner by paying the penalty whatever is chargeable for such delay. Once that is done then get the change of ownership in the registration documents of the bike by visiting to the concerned state transport office. Once it is achieved then based on it one can get from the insurance company change in the name and address in the insurance policy also from the original owner to present owner.