For now, anyway. I have little doubt that Shiro will - for one reason or another - not be piloting the black lion forever. That's when we'll probably see Keith step into the black lion wearing his red uniform, Lance step into the red lion wearing his blue uniform, and Allura step into the blue lion in the pink and blue suit she's been wearing while piloting the castle.
I kinda don't think they'll go that way. The showrunners have thrown plenty of bones to fans of the original, but have clearly signaled a willingness to go their own way rather than be tied to it - a very good thing IMO.
There are a lot of in-universe reasons for Allura not to pilot a lion. She's already a strong leader figure - way more than the original. The castle is a formidable fighting machine of its own right, giving her plenty of opportunity to be badass without having to fly a lion. I'm still hoping that multi-strike scene from the title sequence is a sleeper and will show up eventually, much like the one with Shiro's bayard being activated that didn't appear until the very end of Season 2. Finally, she's the only one who can operate the wormhole generator, something they've needed more than once in combat situations.
I think we'll see a mini-arc with Keith stepping into the leader role, but Shiro will eventually come back. They might put Allura in the blue (or red) lion's pilot seat for an episode or two as a throwback, but I don't expect it to be long-lasting. Who else could step in? Coran perhaps, but the red lion has already rejected him once so it's doubtful. Slav? Would be hilarious, but equally unlikely. The Blade of Marmora's leader is a strong possibility, especially in terms of drama due to Allura's deep mistrust of all Galra...
Anyway, maybe we should start a separate thread.