A little old lady essentially felt for an outcast (7)
I believe the answer is:
ishmael
'for an outcast' is the definition.
(I've seen this before)
'a little old lady essentially felt' is the wordplay.
'a little' becomes 'ish' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'old lady' becomes 'ma' (both can mean mother).
'essentially' indicates the central letters.
The middle letters of 'felt' are 'el'.
'ish'+'ma'+'el'='ISHMAEL'
Can you help me to learn more?
(Other definitions for ishmael that I've seen before include "Moby Dick's narrator, and Abraham's eldest son" , "Bellicose sort" , "Son of Abraham, cast out after the birth of Isaac" , "he survived wreck of whaler" , "Abraham's child" .)