In the shul where I daven, if there is a non-regular with yartzeit and a regular within the year, they will ask the regular if he allows the other guy to daven for the amud. I haven’t heard anyone refuse yet.
If there is a yartzeit, they will also have an extra kaddish just for the yartzeit (the gabbai will announce that it’s a yartzeit kaddish). This is done in different ways, depending on which tefillah it is. By Shacharis, the minhag is usually to say one kaddish yasom at the end, after the yom – they don’t say one after Aleinu. When someone has yartzeit, they’ll say one after Aleinu so there’s an extra one. By Mincha and Maariv they’ll usually say a chapter of tehillim at the end, with a kaddish after. If there’s an extra tefillah said that day (l’Dovid, Barchi Nafshi, etc.) they’ll add the kaddish there.