In this study, the focus was on evaluating the effects of the initial treatment of wood ash and sewage sludge on hybrid alder clones’ aboveground biomass and elemental content. To measure the element concentrations in the tree rings, laser ablation–inductively coupled plasma–mass spectrometry (LA-ICP-MS) was utilized, which is a valuable tool for dendrochemistry research, albeit with some challenges in accurate quantification. One important aspect of the study was the development and comparison of different “in-house” matrix-matched standards for the precise quantification of element concentrations in tree rings. It was found that the commercially available reference materials, IAEA 413 (algae) and IAEA 392 (algae), were the best choices due to their homogeneity. The study also revealed that the use of sewage sludge and wood ash as soil improvers significantly benefited the increase in hybrid alder biomass. However, no significant increase in element content was found in the obtained wood mass, and for some elements, there was a decrease in concentration.