Girl, one facing endless peril (4)
I believe the answer is:
iris
'girl' is the definition.
'one facing endless peril' is the wordplay.
'one' becomes 'i' (Roman numeral**).
'facing' means one lot of letters go next to another.
'endless' means to remove the last letter.
'peril' becomes 'risk' ('risk' can be a synonym of 'peril').
'risk' with its final letter removed is 'ris'.
'i'+'ris'='IRIS'
(Other definitions for iris that I've seen before include "Flower - girl's name" , "Flag - part of eye" , "bit of mince pie" , "Plant - part of the eye" , "Camera diaphragm" .)