Progresses smoothly from university during emergencies (7)

I believe the answer is:

cruises

'progresses smoothly' is the definition.
(to cruise is to move smoothly)

'university during emergencies' is the wordplay.
'university' becomes 'u'.
'during' means one lot of letters goes inside another.
'emergencies' becomes 'crises'.
'u' inserted within 'crises' is 'CRUISES'.

'from' is the link.

(Another definition for cruises that I've seen is " Holidays on water".)

I've seen this clue in The Telegraph.

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