Rush out suddenly to see a girl (5)
I believe the answer is:
sally
I believe this clue is a double definition.
'rush out suddenly' is the first definition.
(I've seen this before)
'girl' is the second definition.
(feminine given name)
'to see a' acts as a link.
(Other definitions for sally that I've seen before include "one in 3 the 12 30 [DROP the DEAD DONKEY]" , "Witty riposte" , "Girl" , "army" , "Sortie; witty retort" .)