Beat cream and cream of tartar in a bowl with an electric mixer until soft peaks form.
Beat mascarpone cheese in a separate bowl using an electric mixer on low speed; slowly beat in confectioners' sugar until fully incorporated. Add pumpkin puree, cinnamon, ginger, nutmeg, and cloves; beat until well combined. Fold whipped cream into pumpkin mixture.
Mix coffee and rum together in a bowl. Briefly dip each ladyfinger into coffee mixture. Arrange a layer of dipped ladyfingers in the bottom of a trifle bowl or serving dish. Cover layer with about 1/3 of the pumpkin mixture. Continue layering ladyfingers and pumpkin mixture.
Cover dish with plastic wrap and refrigerate until set, 3 hours to overnight.