It can be hard to take the advice from people who are no longer in service. Things change, traditions fall aside, the world goes on. But there are some things that don't change. Respect, integrity, compassion, responsibility, and empathy. These are universal. At least they are to me. These are hallmarks of better leaders. Not great ones yet, but better than most.
Respect. For those that have come before you. Generally those who have already done the job probably don't want to do it again. They have been there. done that, and have the plaque for their service. When they provide you advice, the least we can do is listen to what they/we have to say. You don't have to do everything they tell you, but you should be willing to listen. You might be shocked to learn they may actually have a good idea.
Integrity. Taking over 3 days to answer an email is not OK. Acknowledge the request or inquiry. Ignoring someone because you just don't want to deal with them is not acting with integrity. Man up, put your big girl panties on and do what you are supposed to do.
Compassion. Have some compassion for people older then you. Treat the people who have before you with the respect they deserve even if it is only out of respect for their former position. Always let them save face. Remember that you will also be a past someday. How you treat people is how you will be treated later.
Responsibility. Doing your job or what is expected of you will show all the pasts that you are committed and you will probably hear from us a lot less.
Empathy. Before you do something to someone has some empathy. Think about their feelings. When you tell me I am no longer of value process how that's going to make me feel. Maybe there is another way to get what you want without destroying the other person.
Remember that leadership is a process. Respect the past, do good work with integrity, have compassion, take responsibility, and don't forget to practice empathy. And maybe, past leaders like me, won't feel so beat up.