Musical seen by one lecturer during a month off (8)
I believe the answer is:
hamilton
'musical' is the definition.
'one lecturer during a month off' is the wordplay.
'one' becomes 'i' (Roman numeral**).
'lecturer' becomes 'l'.
'during' means one lot of letters goes inside another.
'off' is an anagram indicator.
'i'+'l'='il'
'a'+'month'='amonth'
'amonth' is an anagram of 'hamton'.
'il' inserted inside 'hamton' is 'HAMILTON'.
'seen by' is the link.
(Other definitions for hamilton that I've seen before include "Bermudian capital" , "Emma --, Nelson's lover" , "city down under" , "Motorist" , "Port in Canada - capital of Bermuda" .)