  In this paper, we solve the Dirichlet problem for Orlicz-Sobolev maps between
singular metric spaces that extends the corresponding result of Guo et al.
[arXiv 2021]. As an intermediate step, we develop a version of
Rellich-Kondrachov compactness theorem for Orlicz-Sobolev mappings between
metric spaces that extends a previous result of Guo and Wenger [Comm. Anal.
Geom. 2020]. Another crucial ingredient is an Orlicz-Sobolev extension of the
trace theory for metric valued Sobolev maps developed by Korevaar and Schoen
[Comm. Anal. Geom. 1993].
