If youre coming from Destiny there's important things to know, Warframe will not replace destiny.
Warframe and Destiny similarities start and end at space wizards who kill things with grindy gameplay. While destiny is a methodical looter shooter that takes time and has more hand crafted unique missions and raiding Warframe while having unique options is more of a repetitive power fantasy with more of a story checkpoint system to unlock the next set of grindable gear with in depth and expressive modding to your equipment. One cannot replace the other in any terms of gameplay. Now if you're all about casting abilities and love to use ults in Destiny warframe will scratch that itch, and overall I'll always recommend giving Warframe a go. The community will welcome anyone with open arms, but don't look at it as filling the hole that is Destiny, see it for the new thing that it is and see how ya like it. I'm sad to hear the state of Destiny and for all those looking to Warframe to try out I hope ya love it the way I do, there's certainly plenty to do to keep ya just as busy as Destiny did, just through a different method.
TLDR: Destiny is more methodical while warframes a fun power fest, neither will replace the other. Give it a go though, its free after all.
Edit: I'd like to add, yes I understand we're getting an influx in destiny refugee posting and I get its tiresome. I'm just hoping to temper the expectations of people coming from destiny and maybe answer that question before they post it, maybe prevent a bit of the mass posting with a preemptive general outline of the differences. With the huge shift in the gaming scene it's a bit expected, making this a relevant general discussion. If MODs want it taken down I fully understand and have no complaint. Only hoping to be helpful and welcoming.