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I heard the sentence

> プレゼント **買う心配** がありません

from a Japanese, meaning "We don't worry with buying presents [during
Christmas]"; I was wondering about the `買う心配` part, with a な-adjective
directly following a 辞書 verb; I tried looking in my grammars and googling a
bit, but I'm not sure I ever saw this construction and I still can't find
information about how it work.
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grammar
プレゼント買う心配がありません without particles
The `心配` is a noun here. It's a common pattern of modifying nouns. Try
searching for "modifying noun".

Basically there is a main clause and a sub-clause ending in a plain-form verb.
The verb doesn't have to be in present tense.
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> 「プレセット買{か}う心配{しんぱい}がありません。」

First of all, "present(s)" is 「プレゼント」.

Next, 「買う心配」 is grammatical because 「心配」 is a **noun** in this context; It is
not a na-adjective here. Since it is a noun, the 「が」 can directly follow the
「心配」.

As a noun, 「心配」 can mean "worry/worries", "care", "anxiety", "fear",
"uneasiness", etc.

So, the sentence means:

> "I/We/You have no worries about buying presents!"
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Japanese relative clauses never need particles.

First off, as others have stated, プレゼント買う心配がありません means "(I) don't have to
worry about buying presents" or literally "(I) have no worries about buying
presents" If we swap 心配 with 必要, then we get "I don't need to buy presents."
or literally "I don't have the need to buy presents”.

「プレゼント買う」is basically modifying clause simlar to a gerund meaning “buying
present(s),” Usually gerunds are created by adding の at the end of the verb
like プレゼントを買うのが大好き Meaning “(I) love buying presence.”

But の is not needed when making the modifying clause as the first part of the
relative clause. Here are some other examples.

プレゼントを包む心配ありません。 (We) don't have to worry about wrapping the presents.  
プレゼントを買う夢を見てた。 (I) had a dream about buying presents.  
プレゼントを買った弟がいません。 My younger brother who bought the present isn't here.  

The last example takes a relative pronoun in English which is the bane of
English Learners in Japan. [Here's an article](https://toiguru.jp/relative-
clauses#:~:targetText=%E9%96%A2%E4%BF%82%E4%BB%A3%E5%90%8D%E8%A9%9E%E3%81%A7%E5%AD%A6%E7%BF%92%E4%B8%8A,%E3%81%A9%E3%81%A1%E3%82%89%E3%81%AB%E3%82%82%E5%87%BA%E7%8F%BE%E3%81%99%E3%82%8B%E3%80%82&targetText=%E3%81%A4%E3%81%BE%E3%82%8A%E3%80%81%E9%96%A2%E4%BF%82%E8%A9%9E%E7%AF%80%E3%81%AE,%E5%88%86%E3%81%91%E3%81%A6%E8%80%83%E3%81%88%E3%82%8B%E3%81%A8%E3%82%88%E3%81%84%E3%80%82)
with many examples where Japanese try to figure out how to use them.

You also mentioned missing articles, but the を Is really implied in your
sentence. However it is omitted verbally very often.
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