Complex sentence: When Gorbachev left the ASSR, Ryzhkov remained to coordinate the rescue operation and made several television appearances which increased his standing amongst the Soviet leadership and the people in general.
Split into simpler sentences: When Gorbachev left the ASSR, Ryzhkov remained to coordinate the rescue operations and was present at several television sessions. This increased Ryzhkov's standing amongst the Soviet leadership, and the people in general.