Let’s look at important things here –
Moon - Moon represents Mind, Emotions, Mother, Local Government, Peace of Mind, Home Environment, Water, Milk etc.
Ardra - Ardra is nakshatra of transformation, turmoils and chaotic events. This can be most closely related with accidents and emergencies. For more information on Ardra, please check this link - https://www.astrosaxena.com/ardranaksh.
Gemini - As Ardra is part of Gemini, Gemini sign and its representations become important here. Gemini is the 3rd sign of zodiac belt, so it represents many things related with 3rd house of horoscope like, Communication Skills (either written, oral or even by sign language), Marketing, Business etc. It is a sign basically related with communications and business ideas. Gemini is divided into 2 and half nakshatra of Mrigashira, Ardra and Punarvasu. Gemini's lord is Mercury, which is significator of Communications.
Mercury - As Mercury rules Gemini, Mercury’s position and dignity is important to know about the overall functioning of any planet in Mrigshira/Gemini.
Rahu- As Ardra is ruled by Rahu, Rahu's position and dignity will also have an important role in functioning and results of any planet in Ardra.
Houses Involved – Also, we can’t afford to forget the houses involved as a planet can be ruling different houses and sitting in different house for every person as per ascendant and planet’s position. To know overall affect, we have to consider the houses involved as those areas of life are being impacted.
Interpretation of Moon in Ardra Nakshatra – Now, this is one of the toughest placement of Moon. We can know the reason because of the nature and mythological story of Ardra. As Moon represents Mind and it is the most easily impacted planet and Ardra is all about transformational chaotic event, this shows a mind which always feels to be under chaos and changes. This mind doesn't feel stable and that's why I treat Moon as most important planet because when Mind is not stable then person is not able to take wise decisions in his life and somewhere he gets into chaotic circumstances. As Ardra is ruled by Rahu, it is like there is a shadow of Rahu over mind of person where he can't see things in right perspective and in certain cases person chooses to remain under illusion of Rahu as they feel that illusion is the only reality. In my experience, I have seen people suffering from fear, chaotic dreams and nightmares with this placement but at the same time, if person is inclined towards meditation then things can improve with time. Needless to say that life of Mother of native is also equally chaotic as Moon also represents Mother. At some point of time in life, these chaotic events lead to spiritual growth of person. Positively, their mind can be inclined towards foreign lands and finds peace there. They can be interested in technology related things. Symbolism of Arrow shows that their mind should have a clear goal to keep it focused.
Role of Mercury – Mercury's position will become important in functioning and results of Moon in Ardra/Gemini as Mercury rules Gemini. If Mercury is in good dignity then Moon will have proper direction about the direction of his path or career.
Role of Rahu - Likewise, Rahu's placement is important to guide Moon in right direction.
Other Factors – And of course, we need to consider conjunction, aspects, house lordship, house position and dashas etc to know the exact results of Moon in Ardra. So, we always need to take a holistic view of chart rather than just 1 planetary position.
Conclusion – So, this is how I see Moon in Ardra can work in a chart.