"That person is going to call or write you."
Translation:Cette personne va vous téléphoner ou vous écrire.
Yes, only "cette" is correct here.
ce/cet (masc.) / cette (fem.) / ces (plur.) is a demonstrative adjective, and it can only be used before a noun.
For instance, "this" in "this person" comes right before a noun, therefore it's a demonstrative adjective and is translated by cette: "cette personne"
ça (with the alternative form "ce" when it is the subject of "être") is a demonstrative pronoun, and it can only be used on its own, never before a noun.
"this" in "this is a person" does not come before a noun, therefore it's a demonstrative pronoun and is translated by ça/ce: "c'est une personne"
Thanks relox84. Very helpful This article also helped: https://www.lawlessfrench.com/grammar/indefinite-demonstrative-pronouns/