Price, who played 107 games for Queensland between 1993-94 and 2006-07 and a further 38 for Tasmania, will officially link with Brisbane Heat at the January 1
The reigning BBL champions named Klinger as replacement of new Australia men's assistant coach Andrew McDonald.
England's Liam Livingstone is the first international signing for the Perth Scorchers this season.
Following the IPL, Australia's Big Bash League will now introduce strategic breaks in the middle of matches from the 2019/20 season.
Steyn thus joins fellow South Africans AB de Villiers and Chris Morris in the BBL, with the pair earlier joining Brisbane Heat and Sidney Thunder respectively.
Alex Hales has played 11 Tests, 70 ODIs and 60 T20Is for England.
The WBBL is likely to clash with India's tour of the West Indies, leaving the players with a very limited window towards the end of what will be the fifth season of the WBBL.
Australia's Big Bash League has decided to scrap the boundary count-back rule, to avoid a repeat of the controversial 2019 World Cup final between England and New Zealand.
The next-gen technology of a cricket ball is here. The Big Bash League might see the introduction of 'Smartball', a ball with an embedded microchip.
A total of 56 matches will be played over 42 days, with all teams competing in 14 home-and-away encounters with the final being played on February 8.
WBBL, which will be followed by the ICC Women's T20 World Cup 2020 Australia, will commence under lights at North Sydney Oval on October 18 and end with the Grand Final on December 8.
Last month, reports had emerged that AB de Villiers' management had indicated to BBL clubs that he was interested in playing in the competition in 2019-20.
Shane Watson has been in decent touch this IPL, having scored 243 runs in 11 matches with the highest score of 96 against Sunrisers Hyderabad.
Shane Watson played for Sydney Thunder for four years and captained the side for the past three seasons.
Brisbane Heat general manager Andrew McShea on Thursday said Lehmann would assume his position next week.
Nine of Australia's 15 man squad for the T20 series played at least eleven BBL matches in the 2018-19 edition.
The 35-year-old said that he is playing good cricket and is at the top of his game at the moment that increases his chances of making a comeback.
Finch will lead Australia in the upcoming limited-overs series in India starting February 24 where they would play 2 T20Is and 5 ODIs.
The Aaron Finch led Renegades clinched a thriller win against rivals Melbourne Stars to win their maiden BBL title.
Vettori's exit comes days after his former Kiwi teammate Brendon McCullum announced his BBL retirement from the same franchise.
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