The answer to this question is provided by the European Commission.

Article 2(1)(4) of Directive (EU) 2016/97 defines the concept of "ancillary insurance intermediary" with reference to the following cumulative conditions, in conjunction with the precondition that the intermediary takes up or pursues distribution activities on an ancillary basis for remuneration:

(a) The principal professional activity of the intermediary must be other than insurance distribution.

(b) The insurance products distributed by the intermediary must be complementary to a good or service.

(c) The insurance products offered by the intermediary do not cover life insurance or liability risks, unless that cover complements the good or service which the intermediary provides as its principal professional activity.

It follows that ancillary insurance intermediaries are entitled to offer insurance products, other than life insurance and liability insurance products, which are complementary to a good or service they provide. They can exceptionally offer life insurance and liability insurance only if (1) those are complementary to goods or services provided by the intermediary and (2) the provision of those goods or services constitutes the principal professional activity of the intermediary. An insurance product can be considered as being complementary to a good or service if there is a sufficient temporal and factual connection between the provision of the good or service and the insurance coverage.

With regard to the examples given in the question, car dealers can offer mandatory third party liability (MTPL) insurance as an add-on product to cars sold by them, as the sale of cars is their principal professional activity. Travel agencies could propose liability insurance, possibly as part of a travel insurance package provided that (1) there is a sufficient connection between the insurance product and the travel services provided by the agency and (2) the provision of travel services is the principal professional activity of the agency. The same principles apply to financial agents offering payment protection insurance with life insurance elements as a complement to loans and mortgages offered by them, or to real estate agents who propose multi-risk home insurance including liability coverage to the buyers of homes sold by the agents as part of their principal professional activity. In all such cases, there must be a sufficient temporal and factual connection between the insurance coverage and the provision of the good or service by the intermediary as part of his or her principal professional activity. Any decision will ultimately depend on an analysis of the precise conditions of the insurance policy in the light of the applicable national rules on insurance contract law.

Furthermore, if the insurance product is complementary to loans, mortgages or other financial products, one must take into account that credit institutions or investment firms are explicitly excluded from the definition of ancillary insurance intermediaries.

As for question b) whether a car dealer can offer the renewal of MTPL insurance coverage for the vehicle which it previously sold to the client together with the initial MTPL insurance product or can offer an MTPL insurance product for a vehicle purchased by the client from another car dealer, the answer depends again on the existence of a sufficient temporal and factual connection between the provision of the car and the insurance coverage. In the case of the renewal of a MTPL insurance policy sold to the customer together with the car, it can be assumed that there is still a sufficient connection between the main sales operation and the ancillary insurance sale. However, this is not the case where the car dealer offers MTPL insurance for a vehicle purchased from another dealer. Therefore, the renewal of MTPL insurance coverage for the vehicle which it previously sold to the client falls within the concept of ancillary insurance intermediary as defined in Article 2(1)(4) IDD, something which is not the case for the distribution of an MTPL insurance product for a vehicle purchased by the client from another car dealer.

Finally, it should be pointed out that ancillary insurance intermediaries who are distributing life or liability insurance products under the conditions set out in Article 2(1)(4)(c) IDD are not eligible for exemption from the Directive under Article 1(3) IDD, which applies only to insurance covering the risks of breakdown, loss of or damage to goods, non-use of service or risks linked to travel. They have therefore to comply with the IDD regime for ancillary insurance intermediaries.

Disclaimer provided by the European Commission:

The answers clarify provisions already contained in the applicable legislation. They do not extend in any way the rights and obligations deriving from such legislation nor do they introduce any additional requirements for the concerned operators and competent authorities. The answers are merely intended to assist natural or legal persons, including competent authorities and Union institutions and bodies, in clarifying the application or implementation of the relevant legal provisions. Only the Court of Justice of the European Union is competent to authoritatively interpret Union law. The views expressed in the internal Commission Decision cannot prejudge the position that the European Commission might take before the Union and national courts.