Trees already weakened by Storm Atiyah could be brought down by another blast of Atlantic wind on Tuesday.
Met Eireann has issued a nationwide Status Yellow wind warning - which will be in place until 4pm.
A spokesman said: "Strong and gusty southwest winds will veer westerly early this afternoon with some severe and damaging gusts; heavy squally spells of rain continuing too."
Hail showers and thunderstorms are also expected to hit on what will be a wet and windy Tuesday.
Met Eireann is predicting heavy and "squally" rain showers, while wind strengths could reach gale force in the afternoon.
Storm Atiyah plunged 27,000 homes and businesses into darkness on Sunday as power lines came crashing down.
But most houses, farms and businesses had power restored early on Monday.
ESB predicted most of the 7,000 customers still without power would be back online by last night.
At one point several hundred homes around Inch, Co Kerry, were blacked out and hundreds more in Loughatala, Co. Tipperary and Midleton in Cork.
Most of the other outages were in small pockets in rural areas.
Met Eireann said more strong gusts are expected today.
But they won’t be as strong as the 128km/h recorded at Newport in Co Mayo on Sunday - the highest in the country.
It’s going to be a miserable unsettled week with blustery winds, outbreaks of heavy rain and colder than normal.
Local authority crews were out from dawn yesterday clearing fallen trees, poles and debris from roads in counties Kerry, Sligo, Wicklow, Kilkenny and Longford.
In Ballydavid, on the Dingle peninsula, an entire garden shed and its contents was blown onto the road.
But emergency services breathed a sigh of relief as the storm passed without injuries or loss of life.
A tree blown down by the storm fell on a parked car but there were no occupants at the time.
The Status Orange wind warning for nine counties lapsed at 6am on Sunday.
Irish Rail said trains operated as normal yesterday as they lifted precautionary speed limits on Munster rail services.
Nine flights into Cork Airport were cancelled because of the storm and others diverted to Shannon and Dublin as gusts reach 85km/h.
But services were back to normal on Monday.
