Offenders at first lie badly, tiddly in court (3,6)
I believe the answer is:
old bailey
'court' is the definition.
(famous English courthouse)
'offenders at first lie badly tiddly' is the wordplay.
'at first' says to take the initial letters.
'tiddly' indicates anagramming the letters.
The first letter of 'offenders' is 'o'.
'lie'+'badly'='liebadly'
'liebadly' anagrammed gives 'ldbailey'.
'o'+'ldbailey'='OLD BAILEY'
'in' acts as a link.
(Other definitions for old bailey that I've seen before include "Central Criminal Court in London" , "Courts" , "suitable for trial in London" , "London's Central Criminal Court" .)