It’s also a matter of giving up the unskillful things that possessions, honor, and popularity might cause one to do. Sometimes you’ll find yourself in a position of honor and popularity. What’s one to do? Like AN8.6 points out (thanks @sabbamitta!), practice equanimity.
AN4.25 advises that you remember why you embarked on the spiritual path: to put an end to suffering—not to get caught up in things that age, grow ill, and die.
MN30 says a bit more:
Next, take a person of good family who has gone forth… thinking: ‘I’m swamped by rebirth, old age, and death; by sorrow, lamentation, pain, sadness, and distress. I’m swamped by suffering, mired in suffering. Hopefully I can find an end to this entire mass of suffering.’ When they’ve gone forth they generate possessions, honor, and popularity. They’re not happy with that, and haven’t got all they wished for. They don’t glorify themselves and put others down on account of that. They don’t become lazy and slack regarding their possessions, honor, and popularity, but generate enthusiasm and try to realize those things that are better and finer. They become accomplished in ethics… [etc.]