If your child is completely comfortable in shallow water, then she's ready to conquer her fear of deep water.

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By "completely comfortable," I mean she can front float independently for at least ten seconds, back float unaided for at least thirty seconds, and roll in various ways, propel through the water, bob, and dive for objects. Now she's ready to apply these skills to deeper water.
Shallow water vs. deep water
Ask your child, "What do you think will happen when you try to float in the deep water?" Chances are she'll reply with a resounding "I'll sink!" Assure her that the deep water is the same as the shallow water — it does just as good a job of supporting her. She probably won't be convinced until she experiences it for herself.
How long it takes depends on your child and her level of fear. Age can play a factor too — older children are more willing to take chances and acclimate sooner. Remember to practice patience and don't force her to do anything she doesn't want to do.
Monkey walking

Make your way to the deeper water by holding the gutter or edge of the pool with both hands, moving along one hand at a time. This is called monkey walking. She might want to go all the way to the deepest part, or only to shoulder- or neck-deep water — that's okay, start with whatever she's comfortable with. Each time, encourage her to go a little deeper, even just a few inches further along the wall. If she's not willing, don't force it.
Front float in deep water
Practice the front float in the shallow end first — relaxed, head in a neutral position, arms and legs floating naturally, for ten seconds or more. Then monkey walk toward the deep end to try it, stopping wherever she decides.
Have her hold the gutter, hold her breath, put her face in the water looking at the bottom, and not let go, for about five seconds or more. Ask if she was holding herself up or the water was holding her — she'll likely say the water. If she's ready to let go, make sure she drops her hands into the water (lifting them above the water makes her sink slightly). And remember, the front float doesn't have to be horizontal — if her legs dangle, let them dangle.
Back float and otter roll in deep water
Make sure she can back float in the shallow end completely independently for at least thirty seconds, and practice otter rolls. Convey to her that if she can back float in the shallow end, she can do it in the deep end.
Monkey walk toward the deep end and let her decide where to try it. When she's ready, have her hold the wall, place her belly button against it, put her head back, extend her arms, and not let go. Ask if she feels the water floating her. If she's ready to let go, remind her to drop her hands into the water. When she drifts away from the wall, have her perform an otter roll to get back.
Penguin float
A penguin float is floating vertically with a straight body, legs together, and arms at your sides like a soldier. Ask her what she thinks would happen in the deep end — she'll likely say "I'll sink!"
Demonstrate first: hold the edge with one hand, the other arm at your side, legs together. Hold your breath and let go, keeping your head neutral (looking straight ahead). You may be surprised how buoyant you are — some people end up just below the surface, others float higher. Now it's her turn (if she needs help, do this where you can stand but it's deep enough for her).
Why do a penguin float?
To illustrate, once again, just how buoyant we are (except for very muscular people, or those with very little body fat). It proves we won't drop like a rock to the bottom, even in a vertical position. And if your mouth and nose are just inches from getting air, it must take minimal effort to tread water — exactly right. This isn't a treading-water lesson, but it's a step toward it.
Balloon float
Once she has the penguin float, have her pretend to be a helium balloon. Hold your breath, get down to the bottom in the penguin position, then let yourself rise back up to the surface. (Holding your breath is key.) Now have her try it — it's fun, and she'll probably want to do it again and again.
Bobbing in deep water
Work her up to bobbing in about six or seven feet. Start in chest- or shoulder-deep water, making sure she has a good rhythm of blowing bubbles, then taking a breath, in control for at least fifteen bobs.
Every time she goes under, she should bend her knees and push off the bottom (like jumping on land), arms up when she goes down and down when she goes up. In water over her head, the arm action is more dramatic: starting with arms straight at her sides, sweep them up over her head while blowing bubbles to get down, then sweep them back down to her sides (like an eagle's wings) with the jumping action to get back up for a breath.
More on deep water
Be patient and let her go at her own pace. Other deep-water activities you can do alongside her: have her kick to the deep end with a kickboard, a swimming noodle, or my favorite, the Finis Floating Island — a large mat with holes, so they can see the bottom while lying on top. Many of my students still working on their fear of deep water surprisingly love these activities.
Want a head start? Get my free course — How to Prepare Your Baby for Swim Lessons (0–8 months).