Halfway through Hilary maybe tried crudely interrupting Mark and Mike (7)
I believe the answer is:
midterm
'halfway through hilary maybe' is the definition.
(Hilary term is a term at some universities)
'tried crudely interrupting mark and mike' is the wordplay.
'crudely' is an anagram indicator.
'interrupting' indicates putting letters inside.
'mark' becomes 'm'.
'and' means one lot of letters go next to another.
'mike' becomes 'm' (phonetic alphabet: alpha, bravo, charlie etc.).
'tried' anagrammed gives 'idter'.
'm'+'m'='mm'
'idter' inserted into 'mm' is 'MIDTERM'.
(Other definitions for midterm that I've seen before include "period of pregnancy?" , "Halfway through a period in office" , "Halfway through a pregnancy" , "In the middle of a period of office" , "half way through pregnancy" .)