Crossword Genius

Haunting fear papa’s harbouring dreadful secret? On the contrary (7)

Ross

I believe the answer is:

spectre

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'haunting fear papa's harbouring' is the definition.
I can't judge whether this definition defines the answer.

'dreadful secret? on the contrary' is the wordplay.
'dreadful' is an anagram indicator.
'on' indicates putting letters inside (as in clothing 'on' a person).
'the contrary' becomes 'p' (I can't justify this - if you can you should give a lot more credence to this answer).
'secret' is an anagram of 'sectre'.
'sectre' enclosing 'p' is 'SPECTRE'.

Can you help me to learn more?

(Other definitions for spectre that I've seen before include "after-image?" , "Wraith" , "'Phantom, shade (7)'" , "Narrow ravine" , "Ghost, phantom, apparition" .)

I've seen this clue in The Times.
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