2nd Galveston was in January 1863.
For the next six months the focus of US forces in the gulf was on the Mississippi River.
For the six months after that the focus of US forces in the gulf was on establishing a foothold in Texas but Galveston was considered a hard nut to crack so the landings were attempted first at Sabine unsuccessfully and then at Brownsville successfully; troops were then advanced up the coast getting within about 40 miles of Galveston.
But then the focus shifted back to Louisiana, US troops were drawn off the Texas coast and Grant decided that all that was wanted in Texas was the foothold at Brownsville.
Attention only returned to Texas a year later once the rest of the Confederacy had surrendered.