At first, Elizabeth's dad, with song, can end, concerned with farming (8)
I believe the answer is:
agrarian
'farming' is the definition.
(synonyms)
'at first elizabeth's dad with song' is the wordplay.
'at first' becomes 'a' (gst letter of 'at').
'elizabeth's dad' becomes 'grn' (I can't justify this - if you can you should believe this answer much more).
'with' indicates putting letters inside.
'song' becomes 'aria' (aria is a kind of song).
'grn' placed around 'aria' is 'grarian'.
'a'+'grarian'='AGRARIAN'
'can end concerned with' is the 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 agrarian that I've seen before include "of countryside" , "Relating to cultivated land" , "Ruralist" , "Of agricultural land or its cultivation" , "Land reformer" .)