For years the Scots have complained about darker mornings if the clocks were moved forward, which has stopped the rest of the UK having lighter evenings. If Scotland got its independence I can see no reason why the rest of the UK could not move their clocks to European time so leaving Scotland in a different time zone to the rest of Europe and the UK. If the Scots didn't like it then they have to choose whether they would follow the UK.
If they didn't change I would have thought that this could have an impact on departure times and schedules and even where aircraft were based.