Smith and Warner, who were stood down from their skipper and vice-captaincy roles respectively, received 12-month bans from Cricket Australia while Bancroft was given a nine-month suspension for their part in the incident during the third Test against South Africa in March.
The pair were caught up in the ball-tampering scandal in South Africa and were given year long bans away from the game by Cricket Australia.
Warner spent Sunday morning training young women and girls in power-hitting techniques and T20 cricket at Darwin's cricket oval.
Cricket Australia had urged the trio to play premier cricket to forge good relations in their local community.
Addressing reports of a poor culture within the Australian team, Taylor said: "I don't think the culture is that bad. I think I've learned a valuable lesson in this myself".
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Smith is free to return to the Australian set up for next year's World Cup and Ashes in England, but can not fill a leadership position again until the end of March 2019.
"It's so important for us because we've got a big focus in our strategy to grow our women and girls competition", Mr Morrison said.
Smith is expected to be back in the Australian side for the 2019 World Cup but would not be allowed to resume the position of captain for the mega event.
Justin Langer was named as Lehmann's successor on Thursday and the 48-year-old believes his former team-mate has all the qualities to succeed and earn the trust back of the public.
In April, Warner publicly apologised for his role in the ball-tampering scandal, and said he would do everything he could "to be a better person, teammate and role model".
In the past couple of days, both Smith and Warner have extended their heartfelt gratitude towards their family, friends and fans for having supported them in these tumultuous times.
"I think it's also good to have all the young people see that you can move on if you make a mistake, and go forward", said one parent, Renee Cloughessy.