The ESB says it hopes to have the majority of the 8,000 homes still without power restored by this evening.
Counties Mayo, Sligo, Clare and Limerick are worst affected.
Schools are also reopening today in a number of counties, after being forced to close due to Storm Barra.
Speaking to Newstalk, Siobhan Wynne from ESB Networks says its crews are making good progress:
"The worse effected areas are still along the Western seaboard. Crews are mobilising this morning to attend the remaining faults.
"In addition to that we are now able to redeploy crews from less impacted areas to those worse affected."
She said they also have crews from Northern Ireland Electricity (NIE) helping out as they are looking to get the majority of homes back online by this evening.
— ESB Group (@ESBGroup) December 8, 2021
In a press release released last night, ESB said: "Around 13,000 customers remain without supply, down from around 60,000 customers earlier this morning.
"While poor weather conditions have hampered repair works in some areas, ESB Networks’ crews will continue to work into the night doing everything they can to restore power to as many remaining customers as possible and crews will mobilise again at first light tomorrow.
"Following further strong winds last night and during today, counties along the western seaboard from Donegal to Kerry have been most impacted."
It comes as the impact of Storm Barra is continually being assessed. The storm caused damage across the island over the course of Tuesday and into Wednesday, with thousands of homes still without electricity.
While Wednesday afternoon was calmer in many parts of the country, high winds continue to cause damage and status yellow warnings remain in place in several coastal counties in the north and east.
Met Éireann have forecast much calmer on Thursday with rain moving across the country this morning & early afternoon.
Sunny spells & scattered showers will follow behind sun behind cloud with rain, They are expecting highs of 5-11 degrees.
There will be light to moderate SW winds as well.
➡️ Thursday's Weather Forecast ⬅️
Rain moving across the country this morning & early afternoon 🌧️
Sunny spells & scattered showers will follow behind 🌦️
Highs of 5-11°C 🌡️📈
Light/moderate SW winds. Increasing fresh, as the rain clears 💨
More here 👇https://t.co/9gKN6SVok4 pic.twitter.com/uSFHLODDoB
— Met Éireann (@MetEireann) December 9, 2021