Queen or rook captured? That may be a false move (5)
I believe the answer is:
error
'a false move' is the definition.
(I've seen this in another clue)
'queen or rook captured?' is the wordplay.
'queen' becomes 'ER' (short for Elizabeth Regina ie Queen Elizabeth).
'rook' becomes 'R' (chess abbreviation).
'captured?' means one lot of letters goes inside another.
'er'+'or'='eror'
'eror' going around 'r' is 'ERROR'.
'that may be' acts as a link.
(Other definitions for error that I've seen before include "A mistake or inaccuracy" , "Blunder or mistake" , "Slip, mistake" , "Mistake or fault" , "Slip-up" .)