According to Met Éireann the high pressure will bring more settled and drier weather.
Met Éireann is forecasting some rain and drizzle, especially in the north, but it will also be dry with some spells of Autumn sunshine.
"Remaining settled and dry for most through midweek however it will become more unsettled with a better chance of rain later in the week, and more so over the weekend," Met Éireann said.
Meteorologists at the Met Office are also predicting a decent spell.
"Quite settled with a lot of dry and occasionally bright weather around. However chance of rain for a time Friday morning," is the forecast for Derry.