Is it normal for some hair shedding 4 months in after hair transplant?

In general transplanted hairs will fall out several weeks after surgery before new hairs start to grow. You may still see some hair loss after 4 months.

There is a possibility - due to operation stress - that a number of hairs will fall out in the post-operation phase. This generally temporary occurrence is known as "shock loss", and may last just a few weeks or possibly months. In certain cases, donor hairs and neighbouring hairs may fall out after a hair transplant (for instance when dense packing has been performed). This should not worry patients, as the hairs generally regrow once the shock loss period has ended.

You can shed for several months.  Often, but not always, you recover from this shed.  Consider a follow up for an in person exam.

It is very rare that anyone may experience shock loss of the native hair from hair transplant after four months. The accelerated hair loss may be caused by natural progression of hair loss of your native hair. You need to see your doctor for a follow up and start on a medical hair regiment routine.

Shock loss, or acceleration of your normal hair loss, occurs up to a year after a hair transplant. The best treatement for this is finasteride to prevent this.  See video below