The actress's father passed away Thursday night in Clearwater, FL after a brief battle with an infection -- this according to his grandson, Max, the executor of Ron's estate. We're told he was surrounded by family, and that his death was peaceful.

Max writes of his granddad ... "Ron made so many friends throughout his rich life and we want everyone to know that you all meant so much to him. Thank you for everything that any of you did for him throughout his life."

Ron was a professional musician, and was a trained trombone player who played in jazz bands throughout his life ... including gigging with none other than the father of Scientology leader David Miscavige. Yes, Ron was also a Scientologist himself ... as is Elisabeth.

He actually served as a manager for some big stars over the years too -- including Chick Corea, Isaac Hayes and others. Chick is Elisabeth's godfather, interestingly enough.

While he was born and raised across the pond, he and his ex-wife, Linda, raised Elisabeth and her brother Derek here in the States ... Los Angeles specifically. While Elisabeth has posed for some shots with her dad ... it doesn't appear they were that close of late.

Unclear if Elisabeth is aware of her father's death at this point -- we've reached out to her camp for comment ... but so far, no word back. Ron was 79.