After hairs go into the telogen phase and sheds 3 months later,does new hair start growing straight away or is there a delay between it falling out and a new hair taking it’s place?

It varies with each individual and possibly with each follicular unit. It may also be seasonal (something that we are now observing, contrary to what I previous stated -my apologies).
We really know very little about this area, and some of the comments by doctors that have been in the hair restoration business for years show that they are convinced there is a seasonal component found in hair cycling, like most hairy animals.
