I went up Cloud's Rest from Sunrise TH as part of a longer hike approximately July 9th. There wasn't any water flowing in the creeks that drop from the Sunrise Lakes about 2 mi into the hike. There was water in only 2 places between Sunrise TH and Cloud's Rest: at the tarn about a mile south of the Sunrise Lakes/HSC trail junction and at the small stream shown on Harrison/USGS topos about 0.6mi south of the tarn.
The small stream may well be dry now. It already had a slight green tint 4 weeks ago. The tarn will certainly have water, but be prepared to treat it.