Paul wanted to send Timothy soon, but he would wait until he saw how things would go with himself. He would send Timothy immediately after that. Alternate translation: "I hope to send him immediately after I see how things will go with me"
# I hope to send him
"I plan to send him" or "I expect to send him"
# I see how things go with me
"I find out what happens concerning me" or "I learn what will happen to me"