I would say TAR-ick initially, and would guess that if I saw it on someone of European descent, but if I saw the name on someone of Arab or African descent I would say tar-EEK.
If you're asking what spelling I'd pick for the pronunciation tear-ick, I'd say Terrick is the most straightforward, but I like the look of
Tarek (although I'd initially say it TAR-ek, rhyming with
Marek). Teric or Terik would be another option - T +
Eric /
Erik.