Around 100 people in the Belmullet area remain without power due to strong gales caused by Storm Dennis and it is currently unknown when power will be restored.
The service went this morning for almost 500 customers in the area, according to the ESB Powercheck app.
There are also a number of premises without power in the Greater Galway City area with around 400 without power between Salthill, Spiddal and Oughterard.
Power is expected to return to these premises between 3pm and 4pm.
In Creagh there are over 250 people without power as well as over 400 in the Tuam area.
Power will be restored there between 4pm and 8pm depending on weather conditions.
In East Galway there are hundreds without power with over 300 in Gort, 150 in Loughrea, 200 in Kilcolgan with an estimated restoration time of 8pm.
ESB says it is sorry for the loss of supply and that they are working to repair the fault on the line as quick as possible.