While a large body of work in sentence comprehension has explored how different types of linguistic information are used to guide syntactic parsing, less is known about the effect of discourse structure. This study investigates this question, focusing on the main and subordinate discourse contrast manifested in the distinction between restrictive relative clauses (RRCs) and appositive relative clauses (ARCs) in American English. In three self-paced reading experiments, we examined whether both RRCs and ARCs interfere with the matrix clause content and give rise to the agreement attraction effect. While the standard attraction effect was consistently observed in the baseline RRC structures, the effect varied in the ARC structures. These results collectively suggest that discourse structure indeed constrains syntactic dependency resolution. Most importantly, we argue that what is at stake is not the static discourse structure properties at the global sentence level. Instead, attention should be given to the incremental update of the discourse structure in terms of which "discourse questions" are active at any given moment of a discourse. The current findings have implications for understanding the way discourse structure, specifically the active state of discourse questions, constrains memory retrieval.