Most instructions detailing how to prepare ox heart often say something along the lines of "discard any fat and sinew".
Is there any reason why I shouldnt keep the fat?
In general, when a recipe says 'discard,' it means that the part to be discarded is not to be used in the scope of the recipe. I see no reason why you couldn't save the beef fat for other recipes, it can be refrigerated for about a week or frozen for 2-3 months.
See this answer for tips on using the reserved fat. The sinew I would probably just toss. If you have enough saved, you could put it with animal bones to make stock, as the collagen in the sinew will break down into gelatin, but for me, it's not enough benefit to justify saving all those little bits and storing them.