Queen follows cheeky new student (7)
I believe the answer is:
fresher
'new student' is the definition.
(I've seen this before)
'queen follows cheeky' is the wordplay.
'queen' becomes 'ER' (short for Elizabeth Regina ie Queen Elizabeth).
'follows' means one lot of letters go next to another.
'cheeky' becomes 'fresh' (I've seen this before).
'er' after 'fresh' is 'FRESHER'.
(Other definitions for fresher that I've seen before include "More disrespectful" , "New student - more impudent" , "First-year university student" , "First-year undergraduate" , "First-year college student" .)