While road traffic legislation does not provide for a specific requirement in respect of such events, Article 49 of the Road Traffic (Traffic and Parking) Regulations 1997 (as amended) state that a person in charge of an animal which is being conducted along or on to a road shall take all reasonable steps to ensure that the animal does not obstruct traffic or pedestrians. Enforcement of the Regulations is a matter for An Garda Síochána.
Operational responsibility for individual roads is a matter for Transport Infrastructure Ireland under the Roads Acts 1993-2015 in conjunction with the local authorities concerned.