Seeing as the Beast Pirates were susceptible to spies joining their ranks or affiliates (X Drake and Kyoshiro), other factions may have sent undercover agents to join the Beast Pirates. One person I can see stationing a member of their crew within the Beast Pirates to keep tabs on Kaido and his actions is Doflamingo. It has been established already how shrewd a man Doflamingo is and the extents he goes to in order to protect himself and his status. Information was one of Doflamingo’s most powerful weapons. It allowed him to become a Shichibukai and to keep the World Government at bay and semi-subservient to him (using the CP-0 to trick Law into believing he quit being a Shichibukai). Doflamingo had Monet go undercover in the Dressrosa Palace prior to their invasion and on Punk Hazard to keep eyes on Caesar, a partner in his dealings with Kaido. Given all that Doflamingo has done, it seems natural he would also have had someone positioned at one point in time undercover in the Beast Pirates.
The prospect of Doflamingo using an undercover agent seems more logical when you consider Wano Kuni is a closed border nation where no information involving the actions of the Beast Pirates would reach Doflamingo directly – Kaido residing in Wano Kuni was not common knowledge
illustrated by the surprise reactions from Law and the Straw Hat Pirates when Kin’emon revealed Kaido and his Beast Pirates were in Wano. Only the information Kaido (or King) would want Doflamingo to know would be conveyed to him. If Doflamingo desired unfiltered information regarding Kaido’s movements, he would need to acquire it directly from within the Beast Pirates. Additionally, I believe rather than succumbing to the rumours of Kaido, the
fear Doflamingo has of Kaido is sourced from direct knowledge of Kaido’s actions and the forces under Kaido’s command generated by the information he received from the agent undercover as a Beast Pirate subordinate. As for who Doflamingo would have sent, they is only one person with the skill set able to perform that task – Monet.
There is a massive gap in time after Monet's mission on Dressrosa and before she began her mission on Punk Hazard. Around 4-10 years (I believe Monet's Punk Hazard mission began when Vegapunk was still working at the facilities there prior to the explosion Caesar caused). We know Kaido has been operating in Wano Kuni for 20+ years, so it makes sense if at any point during those 4-10 years, Monet was sent on an undercover mission in the Beast Pirates. Monet would have provided Doflamingo with information concerning the general movements of the Beast Pirates. And may even have brought information to Doflamingo's attention that Kaido was interested in creating an army of Devil Fruit Power users which could have been what led Doflamingo (Joker) to reaching out to Kaido and entering into an arrangement.
Now I don't think it would have mattered if Monet was present in the Beast Pirates ranks or not all the time if she were just a low ranking officer. The Beast Pirates have such a vast organisation that it would have been impossible to keep track of everyone coming and going or those present or not. The Beast Pirates currently number
20,000 pirates (not including the 10,000 members from Orochi’s forces) and even in the past, twenty years ago, when Oden challenged Kaido, the Beast Pirates were still a massive pirate organization with a
thousand members. As long as an individual looks the part, they are recognised as part of the Beast Pirates (i.e. current Raid on Onigashima). This could have been how Monet was able to carry out her role as an undercover agent within the Beast Pirates without having been present in the crew/organisation all the time.
But with Monet being a low ranking Beast Pirate member that would have limited the information she were privy to. And in order to work her way deeper into the Beast Pirate organisation, she would have needed to consume a Zoan Devil Fruit or once it was introduced, a SMILE Fruit. That would have been impossible for Monet due to having a Devil Fruit power already. Monet would not have told the Beast Pirates she already possessed the Yuki Yuki no Mi similar to how she kept it a
secret while working in the Dressrosa Palace. And with Monet unable to progress further with her undercover role within the Beast Pirates, she was reassigned to another undercover mission - Punk Hazard, where she was to infiltrate the secret Marine and World Government research labs led by Dr. Vegapunk and gather information surrounding the Marines secret experiments. This could be the reason why Caesar is so casual when interacting with Monet, because he has already worked with her before.
When Law appeared, Monet found a way to rise above her standing within the Beast Pirates without attracting needless attention to herself. Using Law’s abilities with his Ope Ope no Mi, Monet potentially requested Law to change her arms and legs with that of a bird in order to give a certain faction the illusion that she had consumed a SMILE thus allowing her to rise to the next rank within the Beast Pirates – to the level of Gifter. Such a position would have enabled Monet access to additional information not available to the lesser members of the Beast Pirates (Waiters and Pleasures). Monet could have intended to resume her mission undercover within the Beast Pirates after Law left Punk Hazard.
Without proper reason, Monet’s decision to remove her functioning human limbs in favour of wings, talons and a bird tail seem incomprehensibly odd. I find it hard to rationalise the reason being merely because she liked birds and subsequently desired to fly. It is just suspicious no reason was given. Nothing at all. Monet is a very methodological individual whom takes her duties seriously. If she were tasked with an undercover role within the Beast Pirates, she would without fail have realised the opportunity Law possessed once he appeared on Punk Hazard being a doctor who possessed the Ope Ope no Mi. This could be why upon realising what Law could do, she
suggested Law help heal the injured former Punk Hazard prisoners. Monet wished to gauge Law’s capabilities before allowing him to conduct surgery on herself. Ultimately, Monet using the Harpy form to work her way deeper into the Beast Pirates sounds like an undertaking consistent with Monet’s character and role within the Donquixote Family.
There isn't much to suggest that Monet will appear within the Wano Kuni Arc but it would be a fitting arc for her to show-up in. Wano incorporates many elements of Japanese mythology (stories and yokai) and with Monet being a Yuki-Onna, her appearing in the arc would not be out of place.
Additionally, I have been theorising that the Ice Oni plague Queen developed could have been constructed from research done on Monet's Yuki Yuki no Mi powers (assuming the Beast Pirates captured her on Punk Hazard after viewing the fall of Caesar through the broadcast and brought her to Onigashima). If Queen was part of the rogue scientist group Vegapunk and Judge belonged to 21+ years ago, it would help establish Queen's ability to manipulate the lineage factor. And by Queen knowing how to manipulate the lineage factor, it would explain how he can create something like the Ice Oni plague that mutates the lineage factor within its victims. To me, it just seems suspicious that almost a month after Monet is defeat on Punk Hazard, Queen comes up with a plague that transforms people into Ice Oni which share a resemblance to Monet's Yuki-Onna form. It could be nothing but I thought I'll note that theory as well.