Children's author in study penning playful affair on troublemakers, primarily (8)

'children's author' is the definition.
(Richmal Crompton, author of the Just William books)

'study penning playful affair on troublemakers primarily' is the wordplay.
'study' becomes 'con' (con can informally mean to study).
'penning' is an insertion indicator.
'playful affair' becomes 'romp' (romp can mean something fun or light-hearted).
'on' means one lot of letters go next to another.
'primarily' indicates taking the first letters.
The initial letter of 'troublemakers' is 't'.
'romp'+'t'='rompt'
'con' placed around 'rompt' is 'CROMPTON'.

'in' is the link.