This is going to be a little speculative. As I mentioned in the post about types of assassins, this stuff is very hard to get solid information on, so I’m guessing here.
The credible information I’ve read on assassins doesn’t really talk about teams. It doesn’t mean that there aren’t any out there, but at the end of the day it doesn’t take three people to pull a trigger. Now, a support team makes sense to me. You need people who interact with the client, a source of equipment, prep work (which would include research on the target, schedules, means of gaining access, and other intelligence that could be useful). None of this is stuff that would, automatically be something your assassin would involve themselves in. And, when the hammer falls, their ability to disappear is critically important.
Thing is, a lot of these people would, ultimately, be disposable. Think about it: You’ve been hired to kill someone, you need to know where they go in their daily life. You could do it yourself, and after the guy’s dead, you run the risk of someone remembering you were there… or, you could hire four or five people, each one tails your target on specific days and reports to you. Then, after the target’s dead, the chances that anyone will realize, “wait, there were a bunch of different people following the victim” is almost nil.
There are more specialized skill sets that you can’t just pick off the street. If you need a keycard to a construction site, you can’t just grab someone off the street. If you need a fake ID with an actual history and a dead drop inside a guarded fundraiser, you’re probably not going to be able to use the same guy who got you that keycard. You would need specialists, but not the same person.
Also, long term interaction with someone in criminal enterprise (any long term interaction) is a risk. One of the big things with these top tier assassins is avoiding risks. If you’re working with someone for twelve years, there’s a permanent risk that one day they’ll turn on you, for whatever reason. But, if it’s some random surveillance tech you hired for a job, the risk they pose is much lower.
The professional hits we know about tend to be from snipers. This makes sense, long range precision shooting is a relatively safe way to eliminate someone, and in an urban environment, you have all the time you’d need to clean up your area before you wander off. Also, it’s a really blatant way of killing someone, there’s no question, it’s not just a murder, this was an assassination.
This leaves a question, do these guys also engage in frame executions, staging suicides, or arranging accidents. Killing someone as part of a string of unrelated murders is an old literary trick, but it is a valid tactic if you don’t mind collateral damage. Then, while the police are trying to tie the victims together, the assassin can just wander off.
Street level executions are incredibly hard to pin down, fact is, with most homicide investigations, if there’s no connection between the killer and the victim, and the killer doesn’t leave any blatant evidence, it is almost impossible for police to identify a suspect. This is actually what distinguishes a lot of unsuccessful hitmen from the professional assassins. The amateurs tend to take jobs close to home, making it fairly likely they have some connection to the victim, while the professionals are outsiders that arrive, kill, and leave.
Arranging accidents, is another classic literary trick, the murder that looks like a fatal fluke of circumstances. I’ve never seen anything concrete on these actually happening, but as the article I liked a couple days ago pointed out, it’s almost impossible to prove it doesn’t happen. Even something as simple and blatant as a hit and run. It doesn’t have the, “this was an assassination” plastered all over it in 30.06 shell casings, so, odds are, it will never be tied back to the assassin.
It’s probable that assassins have people they work with, representatives and contacts, but I wouldn’t go so far as to call that a team. But, again, this is speculation on my part, and I really could be wrong here.
If your assassin is part of a government sanctioned operations team, then most of that goes out the window. They would be working with a tightly knit team of operatives, but they’d also have a larger resource base to call on. Their legends would be professionally crafted by whatever agency the worked for, not a convenient forger that could get the job done. Their access to critical intelligence and locations would be handled by actual intelligence officers. Even if they’re alone in the field, they’d still be in contact with their chain of command.
Does gender matter? We don’t know of a lot of female assassins, which suggests that the ones who are out there are incredibly good at their jobs. Also, would you really want to get mouthy at someone that kills people for a living, regardless of their gender? This does end up as a general question about who your characters are, and not a training or background question.
As before, I recommend looking at Michael Mann’s crime films, particularly Heat and Collateral. Then, watch them again with the director’s cometary turned on. Mann has done his homework, and you will learn more about professional criminals than you probably wanted to.