Daytime Brexit broadcast making use of both Left and Right? (13)
I believe the answer is:
ambidexterity
'use of both left and right?' is the definition.
(ability to use left and right hands equally well)
'daytime brexit broadcast' is the wordplay.
'broadcast' is an anagram indicator.
'daytime'+'brexit'='daytimebrexit'
'daytimebrexit' is an anagram of 'AMBIDEXTERITY'.
'making' is the link.
(Another definition for ambidexterity that I've seen is " Having equal use of both hands".)
I've seen this clue in The Times.
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