EF lens compatibility on models beyond the EOS Rebel T5 & T6

[Tko2007]

I am a true amateur. I have a rebel t6 and t5. I mostly shoot hockey games, football, cheerleading and equestrian events. I’m going to be purchasing a 70-200 2.8 tamron lens for these events. My main question is this.

I would like to upgrade to a better canon body what is suggested? Will my existing lenses fit? 
Any information will be greatly appreciated 

thanks

[ebiggs1]

"...  life isn't always that simple ..."

... and that's a fact.

"EF and EF-S lenses can be used on R mirrorless bodies, with an EF/EF-S-to R mount adapter." is too simple! Used, yes, but ........