The acid donates the proton and forms an anion which is called the conjugate base of the acid while the bases accept the proton in order to form the conjugate acid. The strength of the conjugate acid and conjugate base depends on the strength of acid and base....
So we can say that $HC{O_3}^ - $ is the conjugate acid as the carbonate ion cannot be an acid in the reaction. $O{H^ - }$ Is the conjugate base as we can see that it is formed after an acid has donated ${H^ + }$ ions ...