Let’s look at important things here –
Moon - Moon represents Mind, Emotions, Mother, Local Government, Peace of Mind, Home Environment, Water, Milk etc.
Uttara Ashadha Nakshatra - It is a nakshatra of career driven people. People who look for authority in life and are highly ambitious. Please check this link to get more information on Uttara Ashadha Nakshatra - https://www.astrosaxena.com/uanaksh.
Sagittarius - As Uttara Ashadha is part of Sagittarius sign, Sagittarius and things represented by Sagittarius are important here. Sagittarius is the 9th sign of Zodiac Belt, hence it represents many things related with the 9th house of horoscope like Religion, Knowledge, Wisdom, Higher Learnings, Gurus, Teachings from your Father etc. Besides it also represents Coaching, Universities, Professors and Preachers, Higher Wisdom, Written Law of the Land etc. Sagittarius has 2 and half nakshatra which are Mula, Purva-Ashadha and Uttara-Ashadha. Sagittarius' lord is Jupiter.
Capricorn - As Uttara Ashadha is also part of Capricorn sign, Capricorn and things represented by Capricorn are also important here. Capricorn is the 10th sign of zodiac belt, hence it represents many things related with 10th house of horoscope like Law and Order, Government, Authority, Organisation, Discipline etc. Besides it also represents World outside your home and people, Fear and Anxiety etc. Capricorn is consisted of next 2 and half Nakshatra, i.e. Uttar-Ashadha, Shravana and Dhanishtha. Capricorn is ruled by Saturn and that's why it represents Fear and Anxiety.
Sun - As Sun rules Uttara Ashadha, Sun's position and dignity is important to know about the overall functioning of any planet in Uttara Ashadha.
Jupiter - As Jupiter rules Sagittarius, their position and dignity is important to know about the overall functioning of any planet in Uttara Ashadha/Sagittarius.
Saturn - As Saturn rules Capricorn, their position and dignity is important to know about the overall functioning of any planet in Uttara Ashadha/Capricorn
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 Uttara Ashadha Nakshatra – Now, Moon is in a nakshatra which is career oriented or ambitious by nature. So, it represents people who are driven towards success and high ambitions in life. As this nakshatra spreads from Sagittarius to Capricorn, these people take their higher education forward to achieve authority and recognition in life. In Sagittarius section of Uttara Ashadha, they can still be about gaining and sharing their higher education or knowledge but when it is in Capricorn section, then these people can be driven towards high rank, authority and status. They want to make good use of their education and achieve big in career. In Capricorn portion, they can be very hard working too which means they deserve what they achieve in their career. In Capricorn section, person can feel lack of nourishment from Mother or may feel that their Mother is just too strict. It creates a natural disconnect between them and their mother where they are unable to understand each other's point of view. With time, they can become emotion-less as they themselves haven't seen any emotions from others. They can also be inclined towards working in Govt or Legal Field. In Sagittarius section, they can still be inclined towards teaching and guiding others. Here, relationship with Mother can also be better as Moon is in friendly sign.
Role of Sun – Sun placement is important to guide Moon in right direction as it is lord of Uttara Ashadha
Role of Jupiter - Also, Jupiter placement is important to guide Moon in right direction, being Sagittarius lord.
Role of Saturn - Also, Saturn placement is important to guide Moon in right direction, being Capricorn lord.
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 Uttara Ashadha. 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 Uttara Ashadha can work in a chart.