A Parisian going after loud and amusing activities (3)
I believe the answer is:
fun
'amusing activities' is the definition.
(amusing or entertaining activity)
'a parisian going after loud' is the wordplay.
'a parisian' becomes 'un' ('a' in French).
'going after' means one lot of letters go next to another.
'loud' becomes 'f' (short for forte - 'loud' in music).
'un' put after 'f' is 'FUN'.
'and' is the link.
(Other definitions for fun that I've seen before include "Enjoyment" , "Light-hearted pleasure" , "Light-hearted amusement, jollity" , "'Merriment, playfulness (3)'" , "Entertaining" .)