Mrs. happens to be flipping — rang in agitation over nothing! (7)
I believe the answer is:
signora
'agitation over nothing' is the definition.
I can't judge whether this definition defines the answer.
'mrs happens to be flipping rang in' is the wordplay.
'mrs' becomes 'Ag'.
'happens' becomes 'is' (to be can mean to happen).
'to be flipping' shows that the letters should be reversed in order.
'rang' becomes 'nor' (I can't justify this - if you can you should give a lot more credence to this answer).
'in' indicates putting letters inside.
'ag'+'is'='agis'
'agis' reversed gives 'siga'.
'siga' going around 'nor' is 'SIGNORA'.
Can you help me to learn more?
(Other definitions for signora that I've seen before include "Italian madam or Mrs" , "Italian married title" , "wife on the Continent" , "married woman in Florence?" , "Foreign woman" .)