What is the possibility of eyebrow transplant for eyebrow hair that is not growing back after being shaved? (photos)

You need an consultation with a doctor. Most doctors do not transplant hairs to a 4 year old unless there is a compelling reason such as burns of disfigurement.

It is not uncommon for the hair near the site of an injury to take several months to grow.  Often times 4-6 months.  Give this situation more time and the shaved hair is likely to come back.  The scar is different, and depending on the closure hair may or may not grow through the scar to camouflage it.  If the scar is a problem, a scar revision could be done at a later date.

It is important to understand that eyebrow transplanting to fix scars is usually not done in children. Most of the hair that was been lost is temporary and a good portion will regrow over 1 years time. If the scar is visible and not quite right, a scar revision to improve the scar would be the next best step. If some hair does not regrow, eyebrow transplants could be done but usually advisable as a teenager or young adult. The decision to repair a scar with an eyebrow transplant in a child could be done but is not typical. 

Eyebrow transplants using scalp hair requires a special skill in identifying the ‘bend’; that is natural in each transplanted hair. So when put in by the surgical team, the natural curve of the hair must be placed to take advantage of it as it is placed.  It also must be put in laying them flat consistent with your natural eyebrow hairs Too many surgeons without considerable experience can’t seem to get either of these techniques right and if they don’t the eyebrow stick out rather than lay flat as they should.  In your case the darker hair and a slightly bushier eyebrow might help you frame your face, but of course, it is your call 100% as to what you want to look like.