Crossword Genius

A coy girl unhappily accepting Heath’s first minority government (9)

Ross

I believe the answer is:

oligarchy

I'm a little stuck... Click here to teach me more about this clue!

'minority government' is the definition.
The answer and definition can be both groups as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'a coy girl unhappily accepting heath's first' is the wordplay.
'unhappily' is an anagram indicator.
'accepting' is an insertion indicator (inserted letters are accepted).
'first' says to take the initial letters.
The first letter of 'heaths' is 'h'.
'a'+'coy'+'girl'='acoygirl'
'acoygirl' is an anagram of 'oligarcy'.
'oligarcy' going around 'h' is 'OLIGARCHY'.

Can you help me to learn more?

(Other definitions for oligarchy that I've seen before include "Form of government with power held by a few" , "Political system of government by a few people" , "a few men in government" , "Rule of the few" , "Government by small elite" .)

I've seen this clue in The Times.
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