Quiet girl on Irish river (7)
I believe the answer is:
'irish river' is the definition.
(I've seen this before)
'quiet girl on' is the wordplay.
'quiet' becomes 'sh' (both can be said to tell someone to be quiet).
'girl' becomes 'Ann' (woman's name).
(Other definitions for shannon that I've seen before include "Irish banker" , "Irish 10" , "Irish airport" , "Have some nosh, Nan, down by the river" , "One who rendered runaway" .)