Our Rex, up for this show primarily? (6)
I believe the answer is:
crufts
'our rex' is the definition.
I don't know anything about this answer so I cannot judge whether this works.
'up for this show primarily?' is the wordplay.
'up' becomes 'cru' (I can't explain this - if you can you should believe this answer much more).
'primarily?' suggests taking the first letters (I've seen 'primarily' mean this).
The first letters of 'for this show' is 'fts'.
'cru'+'fts'='CRUFTS'
Can you help me to learn more?
(Other definitions for crufts that I've seen before include "Annual international dog show" , "Annual London dog show" , "where there are lots of dogs" .)