Quiet touchdown at last in nameless airport (7)
I believe the answer is:
shannon
'airport' is the definition.
(I have seen 'Irish airport' mean 'shannon' so perhaps 'airport' could also mean 'shannon')
'quiet touchdown at last in nameless' is the wordplay.
'quiet' becomes 'sh'.
'at last' says to take the final letters.
'in' indicates putting letters inside.
'nameless' becomes 'anon' (anonymous).
The last letter of 'touchdown' is 'n'.
'n' placed within 'anon' is 'annon'.
'sh'+'annon'='SHANNON'
(Other definitions for shannon that I've seen before include "River in Irish Republic" , "Major Irish river" , "current in Ireland" , "Irish 10" , "Longest Irish river" .)