Typically when an auto insurance policy discusses an "interested party" it is someone or some organization that has an interest in your vehicle. Therefore, it typically means a lien holder or leasing company that has interest in that you have a current car insurance policy because you have their asset, the motor vehicle being insured. Sometimes a parent, guardian, or co-signer can be listed as an interested party so they are included on all policy correspondence.
You may also be referring to the part of an insurance policy that speaks about putting someone on the policy as an interested party or additional interest. This can also be known as additional insured.
Additional insured or Additional interest means the policyholder may specify any other person or organization for coverage under their auto policy. For example, your children or employees of your company may be added as the Additional Insured on your policy.
So an additional interest or insured is a person or an organization, other than the named insured or covered person, who is protected under the named insured's auto policy. If an auto is leased, the leasing company may want to be listed as an Additional Insured as well as a lien holder or loss payee. This protects the leasing company if it's named in a lawsuit for an accident caused by a policyholder.
Any individual with an interest in your property can ask to be added as a loss payee and/or additional insured. Basically a loss payee is someone who will be paid if there is a loss. For example, you have purchased a new car and have decided to finance the cost of purchase. The finance company or bank you use will ask you to add them as a loss payee to your automobile insurance policy.
If you lease a car the leasing company may be asked to be added as a loss payee and as an additional insured because they are an interested party in the vehicle. Adding your leasing company as an additional insured means that, when it comes to that particular car, the leasing company has coverage under your policy for defense if there is a lawsuit.
If your policy is using the term "interested party" in a different manner than ask your agent what your insurance company means by this phrase so you can completely understand your auto insurance policy.