The recent increase in data and model scale for language model pre-training has led to huge training costs. In scenarios where new data become available over time, updating a model instead of fully retraining it would therefore provide significant gains. We study the pros and cons of updating a language model when new data comes from new languages – the case of continual learning under language shift. Starting from a monolingual English language model, we incrementally add data from Danish, Icelandic and Norwegian to investigate how forward and backward transfer effects depend on pre-training order and characteristics of languages, for models with 126M, 356M and 1.3B parameters. Our results show that, while forward transfer is largely positive and independent of language order, backward transfer can be positive or negative depending on the order and characteristics of new languages. We explore a number of potentially explanatory factors and find that a combination of language contamination and syntactic similarity best fits our results.