Advert, perhaps, shows a songbird flying (9)
I believe the answer is:
signboard
'advert perhaps' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.
'a songbird flying' is the wordplay.
'flying' is an anagram indicator (letters fly around into new positions).
'a'+'songbird'='asongbird'
'asongbird' anagrammed gives 'SIGNBOARD'.
'shows' is the link.
Can you help me to learn more?
(Other definitions for signboard that I've seen before include "Where business name may be displayed" , "where bill can be left?" .)