The organisers of the National Ploughing Championships have said social distancing at the exhibition in September would pose a massive problem and if there is any risk to the public, the event "won't be happening".
Yesterday, the Government confirmed that events with crowds of more than 5,000 will not be licensed up to the end of August.
Speaking to RTÉ's Today with Seán O'Rourke, assistant managing director Anna Marie McHugh said that organisers have initiated contact with the Government and will be guided by its advice.
Ms McHugh said organisers delayed the issuing of trade pack for the exhibition, which was due to be released at the start of the lockdown.
She said engineers would be getting on-site to map it and a decision will have to be made about holding the exhibition by early June at the latest.
Speaking on the same programme, organisers of the Rose Of Tralee festival said they were looking at options to see what kind of event they could offer later this year under social restrictions.
Aimee Keane of the festival said that the selection of entrants has been postponed until June, with just one entrant selected so far in Ohio.
Ms Keane said that organisers are chatting to its partners, teams and volunteers to consider what if any kind of event could be hosted.
She said that up to 100,000 people visit Tralee over the five-day event, which had been planned to take place this year from 21 to 25 August.
The founder and director of the Body and Soul festival said they started the cancellation process of the event yesterday.
Avril Stanley said it was too late to consider rescheduling the event and too much ambiguity around future mass gatherings. She said the clearest and fairest thing to do was to cancel the event.
Organisers of the Great Music in Irish Houses Festival have also announced they are cancelling this year's event.
The festival was due to take place from 7 to 14 June.
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In a statement, they said: "Our hope is that much of this year's programme will be able to take place in 2021, and we are working very hard with artists and venues to make this work."
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Elsewhere, organisers of the Galway International Arts Festival have said they are waiting on updated guidance on large gatherings from the Government, before deciding if it will be possible to stage this year's event.
The 2020 Arts Festival is due to take place in mid-July.
Restrictions on gatherings of more than 5,000 people will be in place until late summer.
Large scale events held during the festival, such as concerts at the Big Top, would typically be licenced for less than 5,000 attendees.
But other public events in Galway city centre during the festival could attract bigger crowds.
The likely continuation of social distancing measures, along with associated spacing concerns in venues of all sizes, would pose significant challenges for the staging of many planned events.
The arts festival organisers said they are awaiting further clarity from the National Public Health Emergency Team on crowd restrictions, which is expected before 5 May.
Last night, management at Galway Racecourse announced that the 2020 summer horse racing festival would not be open to the public.
They are examining whether it would be possible to hold the annual Galway Races behind closed doors at the end of July.
Additional reporting Pat McGrath
