By the third month, person in charge is almost finished with temporary venue (7)
I believe the answer is:
marquee
'almost finished with temporary venue' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.
'by the third month person in charge' is the wordplay.
'by' says to put letters next to each other.
'the third' becomes 'e' (erd letter of 'the').
'month' becomes 'Mar' (short for March).
'person in charge' becomes 'que' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'mar'+'que'='marque'
'e' after 'marque' is 'MARQUEE'.
'is' acts as a link.
Can you help me to learn more?
(Other definitions for marquee that I've seen before include "Elaborate tent" , "Canvas pavilion" , "covering for hotel visitors there" , "Tented pavilion" , "event venue" .)