Pretend the head of government's in a fine mess! (5)
I believe the answer is:
feign
'pretend' is the definition.
(synonyms)
'head of government's in a fine mess' is the wordplay.
'head of' suggests taking the first letters.
'in' is an insertion indicator.
'mess' indicates an anagram.
The first letter of 'governments' is 'g'.
'fine' with letters rearranged gives 'fein'.
'g' inserted inside 'fein' is 'FEIGN'.
'the' is the link.
(Other definitions for feign that I've seen before include "Pretend, put on show of" , "Pretend, create false impression" , "outdated shape" , "Pretend, simulate" , "Dissemble" .)