Let’s look at important things here –
Mars - Mars represents our will power, courage, ability to take actions, aggressive nature, anger, our fighting ability, brother, male friends, a boy friend for a girl, a soldier, an athlete and real estate etc.
Purva Ashadha Nakshatra - It is a nakshatra of higher education, analysis and research. It is also nakshatra of giving care to others. For more information on Purva Ashadha Nakshatra, please read this - https://www.astrosaxena.com/panaksh .
Sagittarius - As Purva 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.
Venus - As Venus rules Purva Ashadha, Venus's position and dignity is important to know about the overall functioning of any planet in Purva Ashadha.
Jupiter - As Jupiter rules Sagittarius, their position and dignity is important to know about the overall functioning of any planet in Purva Ashadha/Sagittarius.
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 Mars in Purva Ashadha Nakshatra – Now, Mars's energy and actions go into taking care and nourishing others especially through education and knowledge as this nakshatra is part of Sagittarius. So, they can be seen as good teachers, guide or coaches. As Mars is an Athlete, this can also show a sports coach. They can be good at rationalization and segregation between good and bad or pure and impure. The biggest problem with Mars in Sagittarius comes with fundamentalism. They can have this approach that my knowledge and beliefs are perfect. Hence, this rationalization or segregation may not be always perfect. It can be at their whims and fancies at times. This is something they need to improve. They can be very competitive in matters of education like they would need someone to compete with them to excel in matters of education. So, this position is good for someone to become a teacher or coach but they can be coaches in sports or any other physical activity plus they need to make sure that they should not become fundamentalist.
Role of Venus – Venus placement is important to guide Marsin right direction, being Purva Ashadha's lord.
Role of Jupiter - Also, Jupiter placement is important to guide Mars in right direction, being Sagittarius 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 Mars in Purva 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 Mars in Purva Ashadha can work in a chart.