Daughter in jail beginning to expect justice (5)
I believe the answer is:
judge
'justice' is the definition.
(I know that justice can be written as judge)
'daughter in jail beginning to expect' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'in' indicates putting letters inside.
'jail' becomes 'jug' (synonyms).
'beginning to' suggests taking the first letters.
The initial letter of 'expect' is 'e'.
'd' placed within 'jug' is 'judg'.
'judg'+'e'='JUDGE'
(Other definitions for judge that I've seen before include "Arbitrator" , "Adjuicator" , "Magistrate" , "Form an opinion of" , "Arbitrate" .)