It depends. There are two likely sets of rules: FIDE (which governs international events) and USCF (which governs United States events.) These rules differ slightly.
Under FIDE rules, the default time is 0 minutes unless otherwise indicated. This means that, rather than start the clock of a missing White player, Black could simply claim immediate victory if White was late unless the tournament rules specified otherwise. Under USCF rules, the default time is one hour, meaning Black could only claim victory after waiting an hour (unless the clock runs out before then. of course.)
Under either USCF or FIDE rules, if Black is present and the default time is not zero, then Black starts White's clock when the round starts, whether or not White is present.
The USCF also has a different rule than FIDE if both players are late. According to USCF rules:
If both players arrive late, the first to arrive must split the elapsed time before starting the opponent’s clock. For example, if the first player to arrive is 40 minutes late, the clocks should be set to reflect 20 minutes of elapsed time on each side.
But under FIDE rules:
...if neither player is present initially, White shall lose all the time that elapses until he arrives, unless the regulations of an event specify or the arbiter decides otherwise.