As in every aspect of life, relationships are two-way. Both parties have a responsibility and work to do to make it work. In the admin/boss working relationship however you do have an edge since it is you who schedules your executive’s calendar. Schedule yourself in for one-on-one meetings with your boss on a regular basis. Each situation will be different, but either short daily meetings or longer meetings once a week will work.
Make your meetings count and come prepared with relevant questions you need answers to or with information your boss needs to know. Also use it as a time to get to know them a little bit better. It makes for a better working relationship when you have respect for each other and respect comes from knowing the other person and appreciating who they are as a person as well as for their position.
Give your boss a reason to have confidence in you. Write down any direction or information they give you when you are meeting with them and follow up on items they have requested previously. Let them know you are going to follow through and get the needed information to get the job done. Once they have that confidence you are off to a great start.
My boss knows that I will act on his requests and my goal will be that nothing is going to get missed. Of course we are human so mistakes will be made, but even in that we can own up to our mistakes and learn from them and move on. You will get a lot of respect from your boss when you do that. I used to joke with my former boss that when he did something good, it was a team effort, and I always referred to those times as we did this or that, but when he did something wrong it was his alone. Of course when you work with someone you take the good and the bad because you are a partnership.