New doubts sorted out, as Pilgrim Fathers sailed (9)

I believe the answer is:

westbound

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'as pilgrim fathers sailed' is the definition.
I can't tell whether this defines the answer.

'new doubts sorted' is the wordplay.
'sorted' indicates anagramming the letters.
'new'+'doubts'='newdoubts'
'newdoubts' is an anagram of 'WESTBOUND'.

'out' is the link.

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I've seen this clue in The Times.

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