She was a school friend of Ben Elton at Godalming Grammar School on Tuesley Lane in Godalming, Surrey; Glaister was in the year below Elton. She attended Chichester College where she studied English and Drama, then trained at the National Youth Theatre, before appearing in Broadway. One of her first major TV appearances was in Blackadder II, which Elton co-wrote.
Glaister appeared in the title role in a stage production of Oliver Twist, alongside long-time friend Ben Elton's Artful Dodger. Notable television roles include three appearances as "Bob" in the Blackadder series and the part of Patricia Farnham, the long-suffering partner of Max Farnham (Steven Pinder), in Brookside. In 1983, she returned to the stage in Daisy Pulls It Off.
She has appeared in several TV series, among them:
- Jane Eyre (1983)
- Blackadder II (1986) "Bells"
- Blackadder Goes Forth (1989) "Major Star", "Private Plane"
- All at No 20 (1986)
- Brookside (1990 to 1995)
- Coronation Street (1999 and 2000)
- Family Affairs (2004 to 2005)
She has also appeared in several films including:
- Buddy's Song (1990)
- The Heart Surgeon (1997)
She also appeared in the play Rent.
Her partner is Simon Nelson. They had a son in October 2003 called Clement Jack Nelson