We present the discovery of seven new planets and eight planet candidates around subgiant stars, as additions to the known sample of planets around "retired A stars". Among these are the possible first three-planet systems around subgiant stars, HD 163607 and HD 4917. Additionally, we present calculations of possible transit times, durations, depths, and probabilities for all known planets around subgiant (3<logg<4) stars, focused on possible transits during the TESS mission. While most have transit probabilities of 1%-2%, we find that there are three planets with transit probabilities >9%.