Overly serious, following whizz in school (2-5)
I believe the answer is:
po-faced
'overly serious' is the definition.
(po-faced means overly prudish or disapproving)
'following whizz in school' is the wordplay.
'following' becomes 'f.' (used when citing page numbers etc).
'whizz' becomes 'ace' (synonyms).
'in' indicates putting letters inside.
'school' becomes 'pod' (I've seen this in other clues).
'f'+'ace'='face'
'face' going into 'pod' is 'PO-FACED'.
(Other definitions for po-faced that I've seen before include "Looking unamused" , "Informally solemn in appearance, like nocturnal vessel?" , "With a disapproving countenance" , "Humourlessly disapproving" , "Wearing a stern expression" .)