There are two main ways to "modify" a noun to more accurately describe it.
One is with verbs: you put a verb expressing a state or quality after the noun. For instance, SuvwI' tIn big warrior. This is not what's happening in your phrase.
The other way is with nouns: you put one noun in front of another noun to narrow the sense of the second noun. This is called a genitive relationship in linguistics, and in Klingon it's called a "noun-noun construction." Your phrase is one of these: tlhIngan SuvwI' Klingon warrior. What kind of warrior is it? A Klingon warrior, not some other kind of warrior.
You can create long strings of noun-noun constructions to get very specific, and you can use entire noun phrases in places of simple nouns.
tlhIngan SoS vav jagh Duj puchpa' DoQmIv bIQ tuj jI'ev
the Klingon's mother's father's enemy's ship's bathroom's sink's hot-water handle
(Notice I snuck a noun phrase, bIQ tuj hot water,* in there, and notice that it uses a verb acting adjectivally after its noun, but as a whole unit it just acts like another noun.)
So: to modify a noun with a verb of quality, put the verb after the noun. To modify a noun with another noun, but the modifying noun in front of the noun.