Can you kindly give me a verb for the following?
It is common sight that a child would want to accompany the parent or an elderly person to wherever the latter goes. If the latter does not take the child with him, the child would be left fretting.
I want a verb for the act of the child described in the bold format.
In AmE, rather than saying "parent or elderly person," we would probably say "parent or caretaker." ("Caretaker" refers to whomever is minding the child at the time - a grandparent, an aunt or uncle, a babysitter, etc.)
It is a common sight - a child wants to accompany his parent or caretaker wherever they go and cries and whines if he is left behind.