yes, the default board will have the search in the header bar.
this site is loosely based on the style called prosilver_se. the default style is called prosilver.
you can choose what style you want from the styles demo here:
https://www.phpbb.com/customise/db/styl ... r/demo/3.2
some will already have the search in the navbar or elsewhere.
there are extensions that will allow you to add more links to the navbar and other areas as well.
try the extensions forums below.
check out the links in that menu bar above you can find just about anything you want/need to know about phpbb there and if you can find it there then probably somebody can answer it for you in the forums.