Question - why do you believe Park Dang-gu will be leader of Songrim when Part 2 begins? I don't see anything…
It's the clothes/look of the two. Park Jin is seen in commoner clothes with a shorter hair cut now while Danggu now was wearing clothes that seemed to represent a higher position. Specifically, the robe he's wearing. We see the leaders wearing those types of robes in AoS. Plus, his hair style isn't playful anymore. It's more serious. I hadn't heard about the belt theory until now. But reading about that makes sense too. It seems like there's definitely been a time leap - probably around 5-6 months or so I would assume. Let's of time for Danggu to take over the role of a leader. He was preparing to become one in AoS part 1 anyways.
My guess is that either Park Jin decided to step down because of what happened with Uk, Naksu, and Jang Kang - loosing and almost loosing them OR he was forced to step down. Most likely he was forced due to the friction between him and the other leaders because of his relationship and history with Uk and Jang Kang.
The more I look at the preview the more it seems like everyone is undercover (Jang Uk, Danggu - even though he'll be the leader now - I'm assuming Park Jin stepped down from his position post Jang Uk death/resurrection incident, Cho Yeon - ready for revenge, CP - pretending to side with Jin Mu to get information, and Park Jin), trying to take down Jin Mu and his minions.
The Queen (the OG) looks like she'll side with Jin Mu because they brainwashed her into thinking that whatever happened to her was because of Jang Kang and Songrim - she seemed to eager to punish Jang Uk in the last episode of part 1. Leading to GoJang working together in secret - to fight Jin Mu and find Naksu. I say this since Mu Deok's body was taken from the lake so I'm assuming no one knows about her whereabouts except for Lady Jin (seeing as it looked like her people). Merely keeping/preserving Mu Deok's body until she confirms her suspicion about the original owner of the body.
I think we'll probably see Seo Yul back home and not in Songrim - he was essentially banned from leaving - he couldn't even make it to Jang Uk's funeral (queue evil Uncle) and he's most probably looking for Naksu (maybe remembering their encounter when they were young to find any clues).
1 
I hadn't heard about the belt theory until now. But reading about that makes sense too.
It seems like there's definitely been a time leap - probably around 5-6 months or so I would assume. Let's of time for Danggu to take over the role of a leader. He was preparing to become one in AoS part 1 anyways.
My guess is that either Park Jin decided to step down because of what happened with Uk, Naksu, and Jang Kang - loosing and almost loosing them OR he was forced to step down. Most likely he was forced due to the friction between him and the other leaders because of his relationship and history with Uk and Jang Kang.
The Queen (the OG) looks like she'll side with Jin Mu because they brainwashed her into thinking that whatever happened to her was because of Jang Kang and Songrim - she seemed to eager to punish Jang Uk in the last episode of part 1. Leading to GoJang working together in secret - to fight Jin Mu and find Naksu. I say this since Mu Deok's body was taken from the lake so I'm assuming no one knows about her whereabouts except for Lady Jin (seeing as it looked like her people). Merely keeping/preserving Mu Deok's body until she confirms her suspicion about the original owner of the body.
I think we'll probably see Seo Yul back home and not in Songrim - he was essentially banned from leaving - he couldn't even make it to Jang Uk's funeral (queue evil Uncle) and he's most probably looking for Naksu (maybe remembering their encounter when they were young to find any clues).