Every depot has a roster. When you first join the depot you normally go into what is called the pool. In the pool you can be given any duty and find out those duties a week in advance. Eventually when a vacancy becomes available you join the roster and you can effectively plan your duties for years, at least until there is a new timetable.
Most drivers join what is called a syndicate (mafia for those that know) who take over your duties and hopefully give you want you want, i.e earlies, lates, certain rest days etc.
Links are like a miniature version of the roster. There is an early link, late link and mixed link which is a mixture of early and late shifts.
The issue with the links is that once you are in, it can be very difficult to get out off. So you could be doing permanent late shifts. This is fine if you like lates but sometimes things change like having children and suddenly you need earlies. Most people want to be in the early link but it’s often filled with the senior drivers. I’ve had drivers leave my depot because they were stuck in a link and moved elsewhere to get more flexibility.
Links are not common in most train crew depots.