Diagrams distributed round Rio, primarily, for carnival (5,4)
I believe the answer is:
mardi gras
'carnival' is the definition.
(Mardi Gras is an example)
'diagrams distributed round rio primarily' is the wordplay.
'distributed' indicates an anagram.
'round' indicates putting letters inside.
'primarily' says to take the initial letters.
The initial letter of 'rio' is 'r'.
'diagrams' with letters rearranged gives 'madigras'.
'madigras' going around 'r' is 'MARDI GRAS'.
'for' is the link.
(Other definitions for mardi gras that I've seen before include "festive occasion" , "Day for 9 acrosses" , "Shrove Tuesday celebration" , "pre-Lent festival" , "Carnival (day)" .)