Poem by second in command at National Theatre (5)
I believe the answer is:
odeon
'theatre' is the definition.
(in ancient Greece)
'poem by second in command at national' is the wordplay.
'poem' becomes 'ode' (ode is a kind of poem).
'by' is a charade indicator (letters next to each other).
'second in command' becomes 'o' (o is the second letter in command).
'at' is a charade indicator (letters next to each other).
'national' becomes 'n' (abbreviation listed in Chambers).
'ode'+'o'+'n'='ODEON'
(Other definitions for odeon that I've seen before include "Ancient Greek building for music" , "classical theatre" , "music performed here" , "Ancient Greek theatre" , "Greek music hall" .)