Army. The man whose arm she is on is a 2-star general. (Major General, IIRC.)
Army General
When an active duty member of the Armed Services dies, a Casualty Assistance Officer is assigned to the family to help them through the funeral, and beyond if required. Obviously, for so important a person as a former President, one has been assigned to Mrs. Reagan. A high-ranking one at that. He's responsible for assisting her through the ceremonial duties that lie ahead. Generally, he'll prompt her when she should stand, what comes next in the funeral service, and what not. Of course, he'll provide all possible assistance, including emotional support, to Mrs. Reagan during the hard days ahead. Barring something unforeseen, he will be with her through the whole thing.
He is the General in charge of the Honor Guard division? regiment? sorry, i don't know the correct word.