Quiet girl on Irish river (7)
I believe the answer is:
shannon
'irish river' is the definition.
(I've seen this in another clue)
'quiet girl on' is the wordplay.
'quiet' becomes 'sh' ('sh' is used to tell someone to be quiet).
'girl' becomes 'ann' (woman's name).
'sh'+'ann'+'on'='SHANNON'
(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" .)