Teklić was born in Split to a family originally from Livno and living in the suburb Solin.
He began his youth career at the local NK Solin and quickly moved to the new-founded Adriatic Split where he spent 5 years at the youth levels winning various tournaments and individual awards.
In the summer of 2015, Teklić, alongside many of his Adriatic teammates signed youth contracts with Hajduk Split.
[3] He established himself throughout the Hajduk B squad and got called-up for senior squad league match of Hajduk against Lokomotiva Zagreb, where he entered as a substitute in the 46th minute, replacing Savvas Gentsoglou.
[5] On 21 July 2023, he signed a three-year contract with Süper Lig club Trabzonspor.