Gitksan (Tsimshianic) is morphologically tenseless, and a covert non-future tense was proposed based on ambiguity between present and past readings observed in a simple matrix sentence (Jóhannsdóttir and Matthewson 2007). Behaviours of the non-future tense in subordinate clauses remain understudied (cf. Todorović 2020), and therefore whether this tense is absolute or relative is an open question. This paper investigates the temporal interpretations of attitude complements, relative clauses, and before/after clauses and argues that the non-future tense is relative. Evidence comes from the distribution of the future marker dim in attitude complements and relative clauses in contexts where the subordinate event time (ET) falls between the matrix ET and the utterance time (UT). Seemingly inconsistent temporal semantics of before and after clauses are unified by setting the evaluation time (EvalT) of the subordinate relative non-future tense to the reference time (RT) of the matrix non-future tense, rather than the matrix ET. The need for an account of before/after clauses to refer to the matrix RT provides indirect support for the existence of a pronominal non-future tense in the matrix clause, even though it is covert. The paper calls for comparison of the Gitksan data to temporal interpretations of subordinate clauses in other morphologically tenseless languages, in the hope of uncovering semantic differences beyond the morphological tenselessness.