Trouble about girl's high-flown writings? (7)
I believe the answer is:
airmail
'high-flown writings?' is the definition.
(writings flown in planes)
'trouble about girl's' is the wordplay.
'trouble' becomes 'ail' (synonyms).
'about' indicates putting letters inside.
'girl' becomes 'irma' ().
'ail' placed around 'irma' is 'AIRMAIL'.
(Other definitions for airmail that I've seen before include "Post going by plane" , "Letters sent up" , "It's marked "par avion"" , "Flying post?" , "I'm a liar (anag)" .)