  We introduce an analogue to the amalgamation of metric spaces into the
setting of Lorentzian pre-length spaces. This provides a very general process
of constructing new spaces out of old ones. The main application in this work
is an analogue of the gluing theorem of Reshetnyak for CAT($k$) spaces, which
roughly states that gluing is compatible with upper curvature bounds. We
formulate the theorem in terms of (strongly causal) spacetimes viewed as
Lorentzian length spaces.
