Abridge Old Testament book, suppressing hard term (9)
I believe the answer is:
trimester
'term' is the definition.
(I know that trimester is a type of academic session)
'abridge old testament book suppressing hard' is the wordplay.
'abridge' becomes 'trim' (both can mean to shorten).
'old testament book' becomes 'Esther' (Esther is a book of the Old Testament).
'suppressing' indicates named letters should be taken away (suppress can mean to conceal or hide).
'hard' becomes 'h' (abbreviation used in pencil classifications).
'esther' with 'h' taken away is 'ester'.
'trim'+'ester'='TRIMESTER'
(Other definitions for trimester that I've seen before include "Period of three months" , "academic session" , "American term" , "part of college year" , "US academic term" .)