Royal couple make a mistake (3)
I believe the answer is:
err
'make a mistake' is the definition.
(to err is to make an error)
'royal couple' is the wordplay.
'royal couple' can mean two replacements for 'royal'.
'royal' becomes 'er' (abbreviation for Elizabeth Regina).
'royal' becomes 'r' (abbreviation).
'er'+'r'='ERR'
(Other definitions for err that I've seen before include "Miscalculate" , "Stray from the straight and narrow" , "Go astray" , "have an affair?" , "Slip up" .)