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' (abbreviation for Elizabeth Regina).
'rook' becomes 'R' (chess abbreviation).
'captured?' means one lot of letters goes inside another.
'er'+'or'='eror'
'eror' placed 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" .)