In this Yonhap article about Secretary Mattis’ recent visit to South Korea, there is blurb that states that General Vincent Brooks is likely to stay on as USFK commander:
Another military source said that during the visit, Mattis also expressed his confidence in the U.S. Forces Korea commander, Gen. Vincent Brooks, who was named under the Obama administration and is likely to continue in his current position after the recent administration change in the U.S. [Yonhap]
You can read more at the link, but I hope General Brooks stays on since I believe he has done a great job as the USFK commander. However, my concern is that President Trump is known for holding grudges and General Brooks did testify to Congress with information contrary to what President Trump claimed during his campaign.