Taking turns to change the country (11)
I believe the answer is:
alternation
'taking turns' is the definition.
(I've seen this before)
'change the country' is the wordplay.
'change' becomes 'alter' (synonyms).
'the country' becomes 'nation' (synonyms).
'alter'+'nation'='ALTERNATION'
'to' acts as a link.
(Other definitions for alternation that I've seen before include "Interchange" , "repeatedly going from one to another" , "going by turns" , "rotation" , "Taking of turns" .)