Geinor was born in Merthyr Tudful and attended Ysgol Gyfun Rhydfelen.
In 1988 she spent the summer teaching drama in California, and then attended the Royal Welsh College of Music and Drama to study stage management. Geinor graduated in 1991 and worked with Dalier Sylw before joining Theatre West Glamorgan as their resident stage manager. In 1996 she was given the opportunity to direct Spam Man, the award-winning play written by Dafydd Llewelyn, at the National Eisteddfod in Bala. Following the success of the production she was invited to direct the Theatre in Education productions at Theatre West Glamorgan, now Theatr na nÓg. In 1998 she became the company’s Artistic Director and has directed over 30 Theatre in Education shows and 10 UK Tours.
Geinor is a playwright and has written 15 plays for the Company. Her most recent plays are Operation Julie and The Fight, currently playing at the Sherman Theatre Cardiff.
Geinor was made an Honorary Fellow of the Royal Welsh College of Music and Drama in 2019 and sits on the board of Creu Cymru.
She lives in Cardiff with her husband, Eric, two children Elliot and Gabriel and their dog Ralff.