First half of specified number leave semi-public body (6)
I believe the answer is:
quango
'semi-public body' is the definition.
(I've seen this before)
'first half of specified number leave' is the wordplay.
'first' is a charade indicator (letters next to each other).
'half of specified number' becomes 'quan' (I am not sure about this - if you are sure you should believe this answer much more).
'leave' becomes 'go' (to go is to depart or leave).
'quan' next to 'go' is 'QUANGO'.
Can you help me to learn more?
(Other definitions for quango that I've seen before include "Government-appointed body" , "Board with members appointed by government" , "Semi-public government board" , "Unelected admin. body" , "Body funded by government to work on matters of public policy" .)