they can reapply to your clan and then you can just accept them or another way is to tell them to go  a certain channel in global chat and once both of you are in there just click on their profile pic and invite them to your clan

Actually if a member was removed from the clan they can not simply re-join. The clan leader or a deputy etc with invite privedges must re-invite them. I only know of one way to do this. I do it in the global chat. So you and the person you want to invite must be on the same channel in the global chat. Then I would just show that I am in the channel by saying hello or something, then they can see you and say hello back. At which time I can click on the response from them and re-invite them. Seems harder than it should be ... but I don't know of any other way to invite. I am my clans leader. "5 LIVES" 

Hope this helps someone  🙂