Around 2,500 homes, farms and businesses across the country, predominantly in the South-East, remain without power after their supplies were cut off during Storm Bram.
ESB Networks said it had moved repair crews from other areas of the country today to assist colleagues in the region to reconnect customers as fast as they safely can.
It said crews will continue to work late into the evening to restore supply but due to the damage to the electricity network, a small number of customers in the region will be without power overnight.
They apologise for the particular difficulty this causes.
The electricity utility had earlier called on the public to report any damage to electricity infrastructure and issued a warning to never touch or approach fallen wires.
In Dublin, a power fault has caused disruption to Luas services this morning, with no service on the Green Line since early Tuesday afternoon.
Red Line services have resumed after being suspended earlier between Smithfield and The Point/Connolly.
A spokesperson for the operators of Dublin Airport said that the storm had a significant impact on the airport's operations, with more than 100 flights cancelled by airlines yesterday.
Graeme McQueen said that while Dublin Airport is expected to be fully open today, there is potential for some disruption.
Iarnród Éireann said that a full schedule of train services will operate on all routes today.
A number of ferry sailings to and from Ireland today have been rescheduled or delayed in the aftermath of Storm Bram.
Irish Ferries said passengers are advised to contact their service provider.
Throughout yesterday, there were some incidents of flooding and fallen trees, particularly in the south of the country, where the storm first made landfall.
54,000 homes and businesses were without power as Status Orange wind warnings were in effect nationwide, with winds reaching 113km/h at Roches Point in Cork.
Blustery showers and isolated thunderstorms are forecast for the north of the country today, with conditions otherwise mostly dry with sunny spells.
Met Éireann has warned of a continuation of unsettled weather for the rest of the week and into next week due to what it calls a "mobile Atlantic flow".
Read more:
Storm Bram brings power cuts, flooding and travel chaos
As it happened: Storm Bram