The two aircraft at KWI belong to United Aviation (Sheikh Hamad Al Sabah) and are in red and white livery if those are the ones you are thinking of.
They have been there for around a year now. The new venture you are referring to is the brainchild of Sheikh Ali Al Khalifa and Sheikh Mishal Al Yusuf and is the second of three such licences to operate issued in Kuwait recently.
PS The two aircraft at KWI are Embraer ERJ "Legacy" jets, on lease I think.