My daughter is going to be 3 years old. After playschool and play in the evening. I give her dinner at 8pm and try to put her to sleep at 9pm. She appears to be tired and exhausted and one can see sleep in her eyes. Still she does not want to go to sleep.
Infact after I put her to bed she will start playing with something or the other. And if I do restrict her to the bed she will lie down and sing all the rhymes that she can think of. She starts talking to me and if I do not reply she will go to the extent of talking to herself. With all this going on she never sleeps before 11pm. So, she is ending up having less of sleep.
My daughter had similar behavior but setting a bedtime routine works and be consistent with it for months. Don't expect a change in a couple of days.
Tell a bedtime story may be it helps
One important thing where I used to go wrong is - never play exiting games before sleep timer. Also do not let your child watch TV just before being put to bed. These things excites the child and she/he will not want to rest.