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 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.
Her most recent production was Operation Julie received an incredible response at Aberystwyth Arts Centre, Theatr Brycheiniog and The Lyric Carmarthen. Geinor is a playwright and has written 15 plays for the Company. Geinor was made an Honorary Fellow of the Royal Welsh College of Music and Drama in 2019.