This is late for independent play to start. This is a learned activity.
This suggests that you start young.
Here are eight tips that have most helped us in encouraging our
toddlers to play independently.
- Start Young.
- Stop Playing For Them.
- Take Their Play Seriously.
- Give Them Your Undivided Attention.
- Connect During Care Giving Tasks.
- Get in Touch With Your Child's Interests.
- Limit Screen Time.
I would add because your child is older that you could parallel play.
Parallel play is a form of play in which children play adjacent to
each other, but do not try to influence one another's behavior.
Children usually play alone during parallel play but are interested in
what other children are doing. This usually occurs after the first
Wikipedia on parallel play
I am suggesting that you do this with her (instead of her doing this with another child -- a level she has already accomplished at school) and withdraw over time in a non-obvious way.
Choose an activity that she enjoys, and will take her time doing and that lends itself to individual 'work'. (Painting, clay, Lego/Lincoln Logs, designing a city, dioramas...) You each have separate items and you sit near her and encourage her while doing your own thing. So (example) she builds a lego house and you build a lego hospital and you talk -- but not touch each other's 'work'.
Prepare something in advance that you can go and do on your own, but that can be turned over to her, if she won't stay on task. After a few minutes, you suggest you'll get both of you a drink of water or turn on some music or perhaps even get a snack or fetch more Lego. This should not be a reward, but something you do normally. She stays because if she gets up -- she can get the water while you keep playing. You go OR she goes. Make the interruptions longer and more frequent (over a period of hours or days -- you have to figure it out by doing it).
- Praise anything she does independently. Be honest and fair -- do not praise her for stuff that is not praiseworthy.
- Make sure she has plenty of opportunities to make choices and that you praise her for making them.
- Ask her opinions on things and listen and praise her ideas.
- When you tell her that you are busy and that she must entertain herself, have some suggestions of things she likes to do, and tell her to choose one/some.
- If she doesn't select one, select one it for her. If she refuses to leave you to your task/self -- make a demand that she does a chore*.
*In time, she'll start noticing that making a poor choice leads to her doing something she does not like doing as much. In the beginning, you may have to help her do those chores -- but make those chores her least favourite. She doesn't gain anything by insisting on your time. You have no need to be mad, she will come around. If she complains about the chore, quietly explain that she could have been doing one of the other choices, but that she choose to let you choose. The benefit is that for a little while, you are going to have a very clean home!