The general rule is to use dynamic programming (Labeling Algorithm) to solve the VRP pricing problem. It has some advantage over solving the mathematical model. DP can yield many columns in each iteration versus the one column that yielded by solving the model. As @Kevin Dalmeijer mentioned you need to be able to solve the pricing problem exactly even if you mainly use a heuristic approach.
Normally, a constructive approach combined with a local search would do the work. I saw examples that solves the pricing problem with GRASP or Tabu Search. But if you are going to develop a branch-and-price algorithm later on you should choose a method that is compatible with the branching rule (e.g. Avoiding some edges or including certain edges in the routes).
Here are some studies that use a heuristic approach combined with DP to solve the pricing sub problem.
1) Archetti, C., Bouchard, M., & Desaulniers, G. (2011). Enhanced Branch and price and cut for vehicle routing with split deliveries and time windows. Transportation Science, 45(3), 285–298.
2) Ozbaygin, G., Karasan, O. E., Savelsbergh, M., & Yaman, H. (2017). A branch-and-price algorithm for the vehicle routing problem with roaming delivery locations. Transportation Research Part B: Methodological, 100, 115-137
3) Dayarian, I., Crainic, T., Gendreau, M. and Rei, W. (2019). A branch-and-price approach for a multi-period vehicle routing problem.
4) Gauvin, C., Desaulniers, G., & Gendreau, M. (2014). A branch-cut-and-price algorithm for the vehicle routing problem with stochastic demands. Computers & Operations Research, 50, 141–153
5) Dayarian, I., Crainic, T. G., Gendreau, M., & Rei, W. (2015b). A column generation
approach for a multi-attribute vehicle routing problem. European Journal of Operational Research, 241(3), 888–906