Father under oath, at first, to transform Greek Prime Minister (10)
I believe the answer is:
papandreou
'greek prime minister' is the definition.
The definition suggests a singular noun which matches the answer.
'father under oath at first to transform' is the wordplay.
'father' becomes 'papa' (papa can mean one's father).
'at first' says to take the initial letters.
'to transform' indicates an anagram.
The initial letter of 'oath' is 'o'.
'under'+'o'='undero'
'undero' with letters rearranged gives 'ndreou'.
'papa'+'ndreou'='PAPANDREOU'
Can you help me to learn more?
(Another definition for papandreou that I've seen is " Member of another 7 [ORDER OF MERIT]".)