Carrot hasn't had her time where she was the main figure of the arc. She was a protagonist in WCI, but it wasn't about her in the same way that Baratie was about Sanji or Drum was about Chopper.
We know that Oda can and has given character focused arcs to nakama after they join. Nami was a travel companion and an unofficial straw hat in the beginning. Whilst orange town gave her a bit of focus, it was not comparable to the special feature the other straw hats got. That arc for her was Arlong Park. Likewise with Robin she joined the crew, but only really became a true member after Enies Lobby where she got her focus arc.
Carrot could follow the trend of the girls in the crew and get her main arc at a later point if she is to join.
That's the problem though, characters who were the main figure get their own character focused arcs, side characters don't.
Side characters only appear in cover pages. Most of the time they only play supporting roles. Carrot would need to reach Yamato Wano levels or Sanji WCI levels of importance to become a main figure in the first place.
Whether or not Carrot can get her own character arc
before (In Wano) or
after (after Wano) she joins the crew, she has to be her own main figure of a arc first. She wasn't in WCI (that was Sanji's arc), and she still isn't now in Wano (Yamato and Momo's Arc).