Cross face of triggered girl (7)
I believe the answer is:
bridget
'girl' is the definition.
'cross face of triggered' is the wordplay.
'cross' becomes 'bridge' (bridging is a kind of crossing).
'face of' indicates taking the first letters.
The first letter of 'triggered' is 't'.
'bridge'+'t'='BRIDGET'
(Other definitions for bridget that I've seen before include "Girl" , "Miss Jones the diarist" , "Saint" , "Saintly woman" .)