Republican in club causes terror (4)
I believe the answer is:
brat
'terror' is the definition.
(both can mean a misbehaving child)
'republican in club' is the wordplay.
'republican' becomes 'r' (abbreviation).
'in' indicates putting letters inside.
'club' becomes 'bat' (as in sporting equipment).
'r' put inside 'bat' is 'BRAT'.
'causes' is the link.
(Other definitions for brat that I've seen before include "child - that's a nuisance" , "A spoiled, badly behaved child" , "Unpleasant child" , "Very dry" , "Irritating youngster" .)