Let’s look at important things here –
Sun - Sun represents Personality, King, Government, Father, Authority, Career, Top Positions, Ego, Self Esteem, Health, Education etc.
Bharani – Bharani is nakshatra of death and re-birth, occult/hidden side of life and instabilities. This nakshatra is also connected with sexuality and attraction. As it is ruled by Venus, the significance of wealth, finance and creativity naturally comes to this nakshatra. For detailed information on Bharani Nakshatra, please check this link -https://www.astrosaxena.com/Bharanaksh .
Aries – As Bharani is part of Aries, Aries sign and its representations become important here. Aries is the 1st sign of zodiac belt, so it represents the things and energy of 1st house of horoscope like Self, Personality etc. Besides that, Aries is the sign of our individuality, our aggression, our actions, our competitive ability etc. Aries is ruled by Mars and it is consisted of 2 and half Nakshatras named Ashwini, Bharani and Krittika.
Mars – As Mars rules Aries, Mars’ position and dignity is important to know about the overall functioning of any planet in Aries.
Venus – Likewise as Venus rules Bharani, Venus's position and dignity is important to know about the overall functioning of any planet in Bharani.
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 Sun in Bharani Nakshatra – Now, when Sun is in Bharani Nakshatra, although it is going away from its exact exaltation degree but it is still in sign of its exaltation. So, it will have good strength throughout Bharani. Now, as Sun represents Career & Authority and Bharani is nakshatra of instability & ups and downs, it shows that these people can go through initial instability in career. They can be working in research oriented field or can have great inclination towards following any occult side of Career. As Sun also represents personality, they can have very secretive or hidden personality. They can also go through initial phase of illusion regarding self or a kind of identity crisis when they don't know much about themselves or their path. They can have major transformation or change in life path. It includes possibility of sudden events and accidents. As Venus rules Bharani, they can be in finance or creativity related fields too but anyhow it will be connected with research work. They can be highly sexual too and professions related with sex, physical beauty, child birth or child care can also attract them. As sign is ruled by Mars and nakshatra is ruled by Venus, they can have very attractive personality.
Role of Mars – And here things become very important. Sun remains in Aries for 30 days and in Bharani for about 13.5 days. Many children will take birth in world during this time. They all can’t have similar life path. This is where position of Aries lord Mars becomes important. Best example is chart of Mark David Chapman (https://www.astrosaxena.com/chapman), who had Sun in Aries/Bharani but Mars was with enemy Mercury and in Paap Kartari Yoga. Hence, Sun in Bharani lost its direction and due to other factors in his chart, he ended up in doing what he did. Actually, in his interview he clearly mentioned that he was a kind of lost soul and had no idea about what he wants to do in life?
Role of Venus– Likewise, Venus's position will become important in functioning and results of Sun in Bharani as Venus rules Bharani. Venus's good position would also impact the results of Sun. Actually, if Mars and Venus both are well placed then person can utilize same transformative energy of Bharani positively else it can be Sun exalted only for namesake.
Other Factors – And of course, we need to consider conjunction, aspects, house lordship, house position and dashas etc to know the exact results of Sun in Bharani. Like in Chapman's chart, he ended up in killing John Lennon during Sun MD only in early life when he was only 25. But if you see his interviews of late 1980s or 1990s, you can't believe that this person has killed someone. It is because he started looking at things with more matured mindset plus dashas changed, his other exalted planets started giving him better results with age. So, we always need to take a holistic view of chart rather than just 1 planetary position.
Conclusion – So, this is how I see Sun in Bharani can work in a chart.