Translation:The young teacher is walking in front of the school.
Sorry, actually, "in front", is "elöl", with a short "ö".
The word "elől", with a long "ő", means "from in front of". As in "(move the obstruction) from in front of the train". "A vonat elől".
And "tanár" and "iskola" are in no relation whatsoever in this sentence.
Who? - "A fiatal tanár"
Where? - "az iskola előtt"
Is doing what? - "sétál"
"Schoolteacher" is "iskolai tanár". But it would be used with some kind of a qualifier:
"általános iskolai tanár" - "elementary school teacher"
"középiskolai tanár" - "secondary school teacher"
It would be "the teacher of the school" in Welsh or Arabic, yes.
In Hungarian, I think you'd get something along the lines of az iskola tanára. (Similar to Turkish okul öğretmeni in that the possessor comes first and the possessed thing has a possessive ending on it.)
But you don't get an "of" relationship in Hungarian simply by sticking two nouns next to each other (with no possessive suffixes around), to my knowledge.
There are various possibilities for the "okul öğretmeni" type of relationship in Hungarian. My feeling is that it is not necessarily a possessor-possessed relationship, but rather a "belongs to" kind of fixed construction, like a compound structure.
Schoolteacher would be "iskolai tanár". So, there is a suffix on "iskola". But Hungarian loves glueing words together into a single word, in which case there may not be anything extra, like a suffix, in the mix. I think that depends on the types of words glued together. A few examples: cipőtalp, kabátgomb, fogkefe, diákszálló, könyvhét, etc.
"Iskolatanár" as a word does not exist, but there is "iskolaudvar", "iskolaév", "iskolakezdés", "iskolaköpeny" and many others, for your enjoyment. :)