Header font change

In the code below on my style.css file I replaced “Trebuchet MS” with “Palatino Linotype”, and shifter Trebuchet MS along without quotes in the pre-code area.
The intention was to change headers from Trebuchet to Palatino, because as you can see the code for h1 (and other headers) doesn’t include font family.
However, it did not work.
Should I also make this change in the ‘body’ area?
Link: https://www.alkpurusha.net/WordPress/about/
Any advice appreciated…

body {
    font: 13px/1.5 "Trebuchet MS",Arial;
}
pre, code {
    font-family: "Palatino Linotype", Trebuchet MS,Monaco,Consolas,monospace;
}

p {
    color: #0B3861;
    font-family: "Trebuchet MS";
    font-size: 13px;
    line-height: 1.6;
}

h1 {
    color: #086A87;
    font-size: 28px;
    margin: 0;
    padding: 0;
}