Around 11,000 homes, farms and businesses remain without power this afternoon after Storm Hannah.
Repair crews have already managed to restore electricity to around 22,000 customers - after 33,000 were impacted at the height of the storm.
Earlier, ESB Networks said the worst affected areas were in Munster.
Clare and Kerry had the highest number of outages, with 19,000 customers affected.
Derek Hynes from ESB Networks said crews have been out since first light this morning to begin restoring power supply.
He explained: "We're looking at around 300 locations where there's damage to our network.
"We're confident that we will have power back to everybody across the course of today.
"Work has started in a lot of areas already, where it's safe to do so."
The utility company said "all available resources" have been deployed to deal with the outages.
They're urging members of the public to never touch fallen or damaged wires, and to report any damage to 1850 372 999.
Most of the outages have been caused by trees falling on overhead lines during the strong winds yesterday.
Weather warnings lifted
Storm Hannah hit the country yesterday afternoon and evening.
It prompted Met Éireann to issue several wind warnings - including rare status red alerts for Kerry and Clare.
All warnings have now been lifted.
The strong winds associated with the storm led to some trees and branches falling on roads, particularly in Munster.
However, it is mainly secondary roads that are affected.
Conditions much calmer this morning after #StormHannah. Debris may still be an issue though on secondary routes in particular so take care if taking to the roads.
— AA Roadwatch (@aaroadwatch) April 27, 2019
The AA's Conor Faughnan said motorists all over the country should be careful when using such routes today.
He noted: "Particularly in Clare and parts of Kerry, we do have a number of secondary roads and incidents of branches down and trees down.
"The big thing is the red warning has gone, but it's still a windy day.
"If you're out and about today, if you're on the secondary road network, it's dangerous."
Clare and Kerry County Council crews, meanwhile, have been working to clear roads across the counties:
Council crews have been active throughout the night and this morning in removing debris and fallen trees from roads across the county. Road users are urged to proceed with care this morning #StormHannah #SafetyFirst pic.twitter.com/0wRGraIRkk
— Clare County Council (@ClareCoCo) April 27, 2019
— Kerry County Council - Comhairle Contae Chiarraí (@countykerry) April 27, 2019
At the height of Storm Hannah, the highest average wind speed recorded was 93 km/h at Mace Head in Galway.
Met Éireann says that area also had the highest gusts at 122 km/h.
Shannon Airport was hit with gusts of 119km/h, leading to a number of flights being cancelled or diverted to Dublin.
— Shannon Airport (@ShannonAirport) April 26, 2019