That lady eloped in the beginning at this place (4)
I believe the answer is:
here
'at this place' is the definition.
(synonyms)
'that lady eloped' is the wordplay.
'that lady' becomes 'her' ('her' refers to a woman).
'eloped' becomes 'e' (this could be a standard abbreviation which I don't know about).
'her'+'e'='HERE'
'in the beginning' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for here that I've seen before include "Hither" , "In attendance" , "To hand" , "Present; I say!" , "The present location" .)