Lodges with fellows over academic period briefly (8)
I believe the answer is:
chapters
'lodges' is the definition.
(chapter is a kind of lodge)
'fellows over academic period briefly' is the wordplay.
'fellows' becomes 'chaps' ('chap' can be a synonym of 'fellow'**).
'over' indicates putting letters inside.
'academic period' becomes 'term' (I've seen this before).
'briefly' means to remove the last letter.
'term' with its last letter taken off is 'ter'.
'chaps' enclosing 'ter' is 'CHAPTERS'.
'with' is the link.
(Other definitions for chapters that I've seen before include "Numbered sections of a book" , "Divisions of a book" , "Local branches of fraternity or association" , "Subdivisions of a written work" , "Divisions of written work" .)