Self-absorbed daughter not prepared to enter pub (7)
I believe the answer is:
indrawn
'self-absorbed' is the definition.
(indrawn can mean introspective)
'daughter not prepared to enter pub' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'not prepared' becomes 'raw' (as in raw food).
'to enter' means one lot of letters goes inside another.
'pub' becomes 'inn' (an inn is a type of pub).
'd'+'raw'='draw'
'draw' inserted within 'inn' is 'INDRAWN'.
(Other definitions for indrawn that I've seen before include "sucked in" , "Breath so sharply" , "Shy; inhaled" , "Taken in, like the breath" .)