罗卓瑶于1957年出生于澳门。她毕业于香港大学，获得英国文学学位。1982年至1985年，她在英国国家电影电视学院学习导演和编剧。她的毕业电影《他们说月亮在这里更饱了》（1985）在芝加哥国际电影节上获得了银牌。1985年回港后，她加入香港电台电视部电视剧组，执导了二十多部单集电视剧。

1988年，罗将目光转向电影，并执导了她的第一部剧情长片《另一半和另一半》。次年，她执导了李碧华编剧的《金莲花轮回》。1992年，她凭借《秋月》获得洛迦诺电影节金豹奖和欧洲艺术剧院协会最佳影片奖。她1993年执导的年代剧《僧侣的诱惑》入围威尼斯电影节金狮奖角逐，并在法国Cr teil国际女性电影节上获得最佳影片奖。

1995年，罗冠聪与丈夫方志强移居澳大利亚，继续她的电影制作生涯。她1996年的电影《漂浮的生活》在洛迦诺电影节上获得了银豹奖，同时在Gij n国际电影节上获得了阿斯图里亚斯大奖和最佳导演奖。虽然2000年的《1967年的女神》在芝加哥电影节上获得了最佳导演奖，但年轻的罗斯·伯恩（Rose Byrne）——当时还是一位鲜为人知的澳大利亚女演员——因在电影中的表演而获得了威尼斯沃尔皮杯最佳女主角奖。2004年，罗冠聪拍摄的纪录片《给阿里的信》（Letters to Ali）讲述了一名年轻的寻求庇护者在澳大利亚的生活，被选为澳大利亚电影史上最伟大的100部电影之一。2009年，她凭借中港合拍的《如梦似梦》（Like a Dream）重返华语电影界。

Law的丈夫Eddie Fong也是她的长期合作者。她的大部分电影都是由方氏编剧和制作的。2010年，他们制作了短片《红土》。

Clara Law Cheuk-yiu was born in 1957 in Macau. She is a graduate of The University of Hong Kong with a degree in English Literature. From 1982 to 1985, she studied directing and screenwriting at the National Film and Television School in the United Kingdom. Her graduation film, They Say the Moon is Fuller Here (1985), won the Silver Plaque at the Chicago International Film Festival. After returning to Hong Kong in 1985, she joined the drama unit of Radio Television Hong Kong’s (RTHK) television division and directed over twenty single-episode dramas.

Law turned her sights on film in 1988 and directed her first dramatic feature The Other Half and the Other Half. She then directed the Lillian Lee Pik-wah-scripted The Reincarnation of Golden Lotus the following year. In 1992, she won the Golden Leopard Award at the Locarno Film Festival and the European Art Theatres Association’s Best Picture award with Autumn Moon. Her 1993 period drama Temptation of a Monk was selected to compete for the Golden Lion Award at the Venice Film Festival and won Best Picture at the Cr�teil International Women’s Film Festival in France.

In 1995, Law relocated to Australia with her husband Eddie Fong while continuing her filmmaking career. Her 1996 film Floating Life was awarded the Silver Leopard at Locarno while collecting Grand Prix Asturias and Best Director prizes at Gij�n International Film Festival. While 2000’s The Goddess of 1967 won Law the Best Director award at the Chicago Film Festival, a young Rose Byrne—then a little known Australian actress—was awarded the Volpi Cup for Best Actress at Venice for her performance in the film. Letters to Ali, Law’s 2004 documentary about the life of a young asylum seeker in Australia, was selected as one of the 100 greatest films in the history of Australian cinema. She eventually returned to Chinese-language cinema with the Hong Kong- Chinese production Like a Dream (2009).

Law’s husband, Eddie Fong, is also her long time collaborator. Most of her films were written and produced by Fong. In 2010, they made the short film Red Earth.