Senior person’s school in America, the reverse of perfect (6-2)

I believe the answer is:

higher-up

'senior person's' is the definition.
(I've seen this before)

'school in america the reverse of perfect' is the wordplay.
'school in america' becomes 'high' (high school).
'the reverse of' says the letters should be written backwards.
'perfect' becomes 'pure' (synonyms).
'pure' in reverse letter order is 'erup'.
'high'+'erup'='HIGHER-UP'

(Another definition for higher-up that I've seen is " Senior person".)

I've seen this clue in The Times.

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