1) Upload your custom font to:

catalog/view/theme/BurnEngine/font/

2) Go to Theme Settings > Custom > Stylesheet and insert this integration code:

@font-face {
    font-family: 'Your new font';
    src: url('../../../catalog/view/theme/BurnEngine/font/new_font.woff2') format('woff2'),
         url('../../../catalog/view/theme/BurnEngine/font/new_font.woff') format('woff'),
         url('../../../catalog/view/theme/BurnEngine/font/new_font.ttf') format('truetype');
    font-weight: normal;
    font-style: normal;
}

You can use FontSquirrel tool to convert your TTF font to WOFF / WOFF2

http://www.fontsquirrel.com/tools/webfont-generator

3) In the same panel you can now style desired elements:

h1 {
  font-family: 'Your new font';
}