Is there a trek that combines the Annapurna Circuit and the eastern Upper Mustang?

Yes you can combine the Annapurna Circuit and the eastern Upper Mustang – in fact, probably the best Nepal trek I have ever done combined these two areas!

On my route I flew into Jomson, hiked up the western side of the Upper Mustang Valley and then back down the eastern side. My original intention was to then cross the Teri La pass to the villages of Nar and Phu just off the Annapurna Circuit and then join up with the Annapurna Circuit. However, we couldn't find any local guides willing to lead us over the Teri La and it later turned out that most people preferred not to cross this because of the real danger of rockfalls (a very experienced trek leader who did do it later told me it was very scary).

So instead, we joined the Annapurna Circuit at Muktinath. We then went clockwise (ie the opposite way to everyone else) over the Thorung La pass. Having already been at altitude in Upper Mustang we were well acclimatised so the pass was easy enough. We then continued down the Annapurna Circuit the opposite way to everyone else until Yak Kharka where we cut across to Tilcho Lake. We camped by the lake shore and then continued west along a little used pass over the Mesokanto La and back to Jomson to make for a neat figure eight trek.

However there's a catch and a very good reason why I wouldn't fully recommend this route: We didn't know until we were fully committed but the Mesokanto La is not a trekking pass, it's a mountaineer's pass that involves descending down two very steep glaciers and crossing some rockfall zones. You need ice axes, ropes and crampons to be safe.

I really very strongly advise against doing this pass, so instead if I were you I would simply hike down the eastern side of Upper Mustang and then meet up with the Annapurna Circuit at Muktinath and then go over the Thorung La pass and follow the Annapurna Circuit clockwise (opposite way to everyone else) as far as you wish.