Governments, for example, welcomed by emirs in trouble (7)
I believe the answer is:
regimes
'governments' is the definition.
(regime can mean a government or system of power)
'example welcomed by emirs in trouble' is the wordplay.
'example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'welcomed by' indicates putting letters inside (letters welcomed inside).
'in trouble' is an anagram indicator.
'emirs' is an anagram of 'rimes'.
'eg' inserted into 'rimes' is 'REGIMES'.
'for' is the link.
(Other definitions for regimes that I've seen before include "Systems of government or courses of treatment" , "Governments in power" , "rules" .)