  We apply the method of multiple Dirichlet series to develop $L$-functions
ratios conjecture with one shift in both the numerator and denominator in
certain ranges for the family of quartic Hecke $L$-functions of prime moduli
over the Gaussian field under the generalized Riemann hypothesis. As
consequences, we evaluate asymptotically the first moment of central values as
well as the one-level density of the same family of $L$-functions.
