I got 4368 rank in clat. My name didn't appear in first allotment list. Is there any chance for my selection in upcoming allotment lists?

Hey Avni!

With 4368 getting admission in an NLU is a really tough call. People having ranks of 1000 could secure a seat only because they had reservation of some sort. So you see how high the cutoffs have been this year.
Some sources have also been saying that there won't be much seats left as most students will lock whatever seats they get. Nobody is willing to let go of a seat be it in any NLU. Its unlikely that you will fetch a seat being in the general category.

Dont lose hope and start searching for alternate private  law colleges imparting good education like IPU,ILS Pune, Ms Ramaiah etc.

Good Luck. Hope it helps.