Will GTA 6 get single-player DLC? History says be careful what you hope for
Nothing has been announced. Rockstar's last story expansion shipped in 2009, and neither GTA 5 nor Red Dead 2 got one.

Short answer: nothing has been announced, and the track record is not encouraging.
The record
Rockstar's last story-mode expansion was The Ballad of Gay Tony in 2009, for GTA IV. That game got two, alongside The Lost and Damned, and both are still held up as the standard for what expansion content can be.
Since then: GTA 5 shipped zero story DLC across thirteen years of support. Red Dead Redemption 2 shipped zero. In both cases the post-launch effort went into the online mode instead.
Why this time might differ
The one structural difference is that GTA 6 launches without an online mode at all. Whatever the studio does in the months after release, it is not shipping GTA Online updates on day one, because there is no GTA Online yet.

That is a gap, not a plan. Read it as a reason the question is open rather than as evidence of an answer.
Sources
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