Girl getting the first rise in a job (7)

I believe the answer is:
mission
'a job' is the definition.
(thesaurus)
'girl getting the first rise' is the wordplay.
'girl getting' becomes 'miss' (I can't explain this - if you can you should give a lot more credence to this answer).
'the first' becomes 'noi' (I've seen this in other clues).
'rise' says the letters should be written backwards.
'noi' back-to-front is 'ion'.
'miss'+'ion'='MISSION'
'in' is the link.
Can you help me to learn more?
(Other definitions for mission that I've seen before include "Ministry sent by a church to spread its teaching" , "In religious campaign" , "Vocation; embassy" , "1996 Tom Cruise spy film -- extremely dangerous assignment" , "Task assigned to be done" .)
