Thank you very much for your query to Ireland Reaching Out. The Whitegate you mentioned is the same Whitegate on the Clare/Galway border. There is just the one Whitegate.
You are more likely to receive more replies if you keep the query open on the message boards rather than in a private email address. Other people in these communities might be viewing your query and the more information other people add to the message, the more likely you will get more information.
If you know the name of the ship Patrick emigrated on, then you will hopefully be able to find more information about him. This information was generally detailed at the port of arrival rather than the port of departure.
Have you considered checking land records such as the Tithe Applotment Books (1823-38) or Griffith's Valuation (1848-64) for more detailed information?
Best of luck with your research!