Former student diary containing note identifying geometrical shape (6)
I believe the answer is:
oblong
'geometrical shape' is the definition.
(old-fashioned term for a rectangle)
'former student diary containing note' is the wordplay.
'former student' becomes 'OB' (abbreviation for 'Old Boy').
'diary' becomes 'log' (log can mean a record or diary).
'containing' indicates putting letters inside.
'note' becomes 'n' (abbreviation).
'log' placed around 'n' is 'long'.
'ob'+'long'='OBLONG'
'identifying' acts as a link.
(Other definitions for oblong that I've seen before include "Cab" , "Shape that's broader than long" , "Something with an elongated rectangular shape" , "Rectangular two-dimensional figure" , "Strip for planes" .)