Abstract To predict shrub responses under climate change in tundra, we need to understand how thermal conditions and herbivory contribute to growth. We hypothesise that shrub growth increases with thermal conditions and precipitation, but that this increase is counteracted by insect herbivory, and that these climate–insect herbivory relationships are modified by both browsing and plant age. We use empirical dynamic modelling (EDM) to analyse a 20‐year time series on willow Salix phylicifolia shoot growth, growing degree days, summer precipitation and herbivory from an experiment at forest–tundra ecotone. The experiment includes manipulations of avian and mammal browsing (fences) and ramet age (pruning to rejuvenate willows). Negative effects of insect herbivory on willow shoot growth were intensified during warmer years, whereas increasing precipitation led to reduced effects. Moreover, the effect of insect herbivores on shoot growth varied with ramet age and vertebrate browsing: younger ramets generally experienced less negative insect herbivore effects, whereas ptarmigan browsing was associated with more positive temperature effects on shoot growth, and reindeer browsing with more negative effects of insect herbivory and precipitation. Synthesis. Our findings show that the negative effects of insect herbivory on shoot growth likely intensify under warmer thermal conditions, but that increasing precipitation can counteract these effects. Moreover, changes in thermal conditions, precipitation and vertebrate browsers all have predictable, albeit complex and nonlinear, effects on shrub growth, highlighting the importance of long‐term experimental data and flexible analytical methods such as EDM for characterising climate and community interactions in artic systems.