A - Thanks for asking. We really won't see much change in how things work at all, because immediately after a bishop given a new assignment to a new diocese (or retires), he becomes the administrator of his former diocese (in this case, Bishop Aymond is currently the administrator of the Diocese of Austin) until he is installed in the new diocese.
The "episcopal see" of Austin will not be without someone over it through this process. Canon 416 reads:
An episcopal see is vacant upon the death of a diocesan bishop, resignation accepted by the Roman Pontiff, transfer, or privation made known to the bishop.
The canons that follow 416 then explain that the bishop is named administrator of the diocese he has just left until he takes possesion of his new see. If there is no new bishop named by the time he leaves, a priest (or another bishop if there are other bishops in the diocese) administrator will be named to replace him in the interim within eight days by the college of consultors within the diocese (the presbyteral council). If they fail to elect someone administrator within eight days, then the metropolitan (archbishop of the area) will name one.
The administrator has limited duties and cannot take on financial responsibilities. Their role is to keep things going until the new bishop takes over. They also are forbidden to have any "innovations" during the vacancy of the bishop.
This process is an ordinary part of the life of the Church. Pray hard during it.
One of the interesting things is that immediately upon having a bishop notified of a new assignment to a new diocese, the office of vicar general (and other administrative offices) ceases. We just had Fr. Mike Sis (our former pastor) named co-Vicar General a few weeks ago. He is no longer vicar general.