Coin short clue about an administrative body (7)
I believe the answer is:
council
'an administrative body' is the definition.
(I've seen this before)
'coin short clue about' is the wordplay.
'short' means to remove the last letter.
'about' is an anagram indicator.
'clue' with its last letter taken away is 'clu'.
'coin'+'clu'='coinclu'
'coinclu' anagrammed gives 'COUNCIL'.
(Other definitions for council that I've seen before include "Elected body organising, say, county affairs" , "Body found in town hall" , "Committee, to arrange the business of a society, say" , "Town or county assembly" , "Body of lawmakers" .)