How does missing an important feature affects the feature importance of remaining features in the model?

I am creating a linear regression model for energy usage in a food processing plant. Unfortunately, I don't have the historical data for one of the critical features (I know it is important from experience). If I go ahead with the modelling excluding this feature, what will be its impact on my model performance and especially on the feature importance. Can I trust the feature importance in the absence of this feature, or would the model over attribute the importance for the existing features

Your help is highly appreciated.