Random piece of period drama (3)
I believe the answer is:
odd
'random' is the definition.
(synonyms)
'piece of period drama' is the wordplay.
'piece of' says the answer is hidden in the clue.
'ODD' is hidden in the letters of 'period drama'.
(Other definitions for odd that I've seen before include "Weird" , "Extraordinary" , "like twenty two [FIFTEEN]? Yes and no!" , "Queer" , "Funny" .)