Annoyed with nation’s sport (5-7)
I believe the answer is:
cross-country
'sport' is the definition.
(cross-country running)
'annoyed with nation's' is the wordplay.
'annoyed' becomes 'cross' (I've seen this in another clue).
'with' is a charade indicator (letters next to each other).
'nation' becomes 'country' (synonyms).
'cross'+'country'='CROSS-COUNTRY'
(Other definitions for cross-country that I've seen before include "Rural running event" , "Running sport" .)