Hestia was the goddess whom, to the ancient Greek citizenry was paid such respect, that she is the first paid homage at every meal, before any other god. She was the sister of Zeus, himself, and when she approached him to tell of her wish to be of eternal service to Mt Olympus, even forsaking marriage to do so, her brother was touched. He soon made her the chief administrator of all processes and resources of the home of the gods. The Hestia Instinct is then, the "sister instinct" that draws vitality and passion from connecting with other women on a journey or for a cause.
She was the hub of activity, the ultimate manager, confidante, and police officer of heaven, to the point that not any other deity could check out their weapons or tools without first approaching her for permission.
If there is any doubt in your mind what is deep in the psychology of the rise of women to economic and occupational power today, it very well may be the instinct of Hestia in them - sisterhood, organization, and working as one for the common good. Within the past several years, women for the first time in United States history outnumbered men in the workforce. Maybe you have noticed your workplace filled with more women than in any decade past, the workings of the corporation humming with their planning, and efficiency, with the perfect allocation of resources in fairness in most cases.
This is Hestia, (or the Roman, Vesta) the goddess of friendship among women, bonds of sisterhood like those of Bluebeard’s sister-in-law or Psyche’s sisters - whose opinions have the power to plumb the depths of his inner intentions, then to make or break the man’s reputation, his public identity, and his livelihood therein. Part of being a gentleman is knowing how to either please the Hestia Instinct in women, or to deal with it appropriately, and with mutually respectful boundaries.
To women, Hestia is the salve of sisterhood on the wounds of a breakup, or of infidelity, an eternal spring of femininity to tap into, and to give generously to, and the real spirit of modern feminism.
The Hestia Instinct might be seen in Step 2 of Sexual Attraction, when the needs and connection with a woman's female friends need to be reconciled with the needs and connection to a new romantic interest. He must respect the friends, or risk losing the relationship, and her honesty and loyalty to the needs of the community were what caused her to rise up to chief administrator under Zeus and Hera on Mt Olympus.
An important feature of early romance is for the two partners to remember that when possible, all the features of one's femininity or masculinity must be stoked, if possible, for maximum masculinity, femininity, or passion in the partner. Which amplifies their shared passion, and the vitality they will draw from the relationship. A woman needs to make use of her friendships and have the man respect and support them.