A conjugate acid will change to conjugate base by accepting one proton.
According to Brønsted–Lowry acid–base theory, an acid is a specie which has tendency to lose an electron while a base is an specie which has tendency to accept an electron.
Hence a conjugate pair is a pair of acid and base which are differ in only one proton.
HCl is acid which is a part of conjugate pair.
If HCl lose a proton it changes to Cl- which is conjugate base of an HCl acid. And this conjugate base will change to conjugate acid by accepting one proton.
Hence the reaction is:
Cl- + H+ → HCl