Point to mine having the sobriquet (7)
I believe the answer is:
Here is my best explanation:
'sobriquet' is the definition.
(I've seen this before)
'point to mine having the' is the subsidiary indication.
'point' becomes 'e' (E is an example).
'to mine' becomes 'pit' (down the pit).
'having' indicates putting letters inside.
'pit' enclosing 'the' is 'pithet'.
(Other definitions for epithet that I've seen before include "Descriptive term used to express a real quality", "Descriptive term or short phrase", "Adjective expressing some quality of a person", "A descriptive word or phrase", "The 23: an -- for Richard I", "Descriptive word or phrase added to a name", "Descriptive work or phrase", "Sobriquet", "Descriptive adjective" and "Phrase expressing some quality of a person or thing".)