漢字が持つ is a relative clause. It has a gap in object position:
The gap is filled semantically by the following noun phrase 体系的なつながり:
① 漢字-が 体系的なつながり-を 持つ
② [ 漢字-が ＿＿＿＿＿＿＿＿-
を 持つ ] 体系的なつながり
These can be translated into English:
① Kanji have a systematic relationship.
② the systematic relationship [ which kanji have ＿＿ ]
The details are different in English because of articles and relative pronouns, but hopefully you can see the parallel:
In example ① we have an independent clause (a complete sentence).
In example ② we come up with a noun phrase by relativizing the clause; we pull out one of the arguments and turn it into the head noun that the clause modifies.