Sums of values of nonprincipal characters over a sequence of shifted primes

For a nonprincipal character $\chi $ modulo $D$, we prove a nontrivial estimate of the form $\sum _{n\le x}\Lambda (n)\chi (n-l)\ll x\exp \{-0.6\sqrt {\ln D}\}$ for the sum of values of $\chi $ over a sequence of shifted primes in the case when $x\ge D^{1/2+\varepsilon }$, $(l,D)=1$, and the modulus of the primitive character generated by $\chi $ is a cube-free number.