Pilots can fly a bit faster but usually we're talking 0.01 mach or so. Occasionally the airline may encourage them to fly that bit faster to try and get back on schedule. A slight change in speed over a long sector can make quite a bit of difference. This has to be offset by the increase in fuel burn and the operational impact of having the aircraft delayed.
Thankfully schedules are usually sufficiently padded so that an aircraft will arrive roughly at the scheduled time even if departing a bit later than planned.