Depart to stare at popular website (6)

I believe the answer is:

google

'popular website' is the definition.

'depart to stare' is the wordplay.
'depart' becomes 'go' ('go' can be a synonym of 'depart').
'to stare' becomes 'ogle' (I've seen this before).
'go'+'ogle'='GOOGLE'

'at' acts as a link.

(Other definitions for google that I've seen before include "Widely-used search engine for internet" , "Search online" , "Popular search engine for internet" .)

I've seen this clue in The Times.

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