Taunt European going after rock (4)
I believe the answer is:
gibe
'taunt' is the definition.
(I know that gibe is a type of taunt)
'european going after rock' is the wordplay.
'european' becomes 'E' (abbreviation e.g. EU).
'going after' means one lot of letters go next to another.
'rock' becomes 'gib' (both are nicknames for Gibraltar).
'e' after 'gib' is 'GIBE'.
(Other definitions for gibe that I've seen before include "Hurtful remark" , "A jeering remark" , "Jeer, barb" , "Barb, dig" , "Jeer, mock" .)