Country Dane is in travelling round Odense, primarily (9)
I believe the answer is:
indonesia
'country' is the definition.
(Indonesia is an example)
'dane is in travelling round odense primarily' is the wordplay.
'travelling' indicates anagramming the letters.
'round' indicates putting letters inside.
'primarily' indicates taking the first letters.
The first letter of 'odense' is 'o'.
'dane'+'is'+'in'='daneisin'
'daneisin' anagrammed gives 'indnesia'.
'indnesia' enclosing 'o' is 'INDONESIA'.
(Other definitions for indonesia that I've seen before include "Asian country, capital Jakarta" , "State" , "I said none (anag) - country" , "part of Asia" , "An ionised country of South East Asia" .)