Slip made by Queen introducing Republican (3)
I believe the answer is:
err
'slip' is the definition.
(I've seen this before)
'by queen introducing republican' is the wordplay.
'by' says to put letters next to each other.
'queen' becomes 'er' (abbreviation for Elizabeth Regina).
'introducing' says to take the initial letters.
The first letter of 'republican' is 'r'.
'er' put next to 'r' is 'ERR'.
'made' is the link.
(Other definitions for err that I've seen before include "Boob" , "Miscalculate" , "Transgress" , "Make a wrong move" , "'to... is human,to forgive divine'" .)