Republican coming into club causes terror (4)
I believe the answer is:
brat
'terror' is the definition.
(both can mean a misbehaving child)
'republican coming into club' is the wordplay.
'republican' becomes 'r' (abbreviation).
'coming into' means one lot of letters goes inside another.
'club' becomes 'bat' (as in sporting equipment).
'r' placed into 'bat' is 'BRAT'.
'causes' is the link.
(Other definitions for brat that I've seen before include "Troublesome child" , "annoying young fellow" , "Very dry" , "Nasty little kid" , "Young rascal" .)