Metal Fighter Miku, Battle Athletess Daiundoukai (TV) Recommendations
Futuristic, unusual competitive sport and main character growing into the role is what these two anime have in common.
In Metal Fighter Miku it's Neo Pro-Wrestling - a version of pro-wrestling where fighters (all female) use metal suits.
In Battle Athletess Daiundoukai it's a mix of futuristic versions of some well known sports (e.g. zero-G lacrosse).