Day 4 Struggles

My 4 day old is CONSTANTLY feeding. Particularly through the night. He won’t even stop for a proper sleep and generally falls asleep for short periods (5-10 mins) when feeding. He then immediately starts crying for another feed if I wrap and put him into his bed. He will sleep for longer periods in my arms if I let him after feeding.

Will this improve when my proper milk supply comes in? Or am I doing something wrong? Is he just too clingy?