Daughter is chased by pig that’s let out (8)
I believe the answer is:
disgorge
'let out' is the definition.
(to disgorge is to release or pour out)
'daughter is chased by pig' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'chased by' says to put letters next to each other (some letters chase after others).
'pig' becomes 'gorge' (I've seen this before).
'd'+'is'+'gorge'='DISGORGE'
'that's' is the link.
(Other definitions for disgorge that I've seen before include "yield under pressure" , "So rid egg? (anag)" , "Throw up, regurgitate" .)