parsnip and its extension packages generally "only" wrap other modelling packages, so if you can pass coefficients depends on the underlying engine. For a Cox PH model with the survival package, you could pass the model coefficients as the initialization values and then restrict the number of iterations for the estimation process to 0. So something along these lines:
# with the survival package directly
engine_fit <- survival::coxph(formula, data = train_dat,
init = model_coef,
control = survival::coxph.control(iter.max = 0))
# wrapped in the tidymodels framework
censored_fit <- proportional_hazards() %>%
set_engine("survival", init = model_coef,
control = survival::coxph.control(iter.max = 0)) %>%
fit(formula, data = train_dat)