a gift of grace: God's grace made concrete in a particular person, moment, or community
This word is built directly on the Greek word for grace, with an ending that turns it into the noun for the result of an action. So if grace is God's free favor, this word is that favor made concrete: grace that has actually landed somewhere, taken a specific shape, and done something. It is almost entirely a word of the apostle Paul. He uses it sixteen times, with one more use in 1 Peter, and in doing so he effectively created its meaning, because the word was rare and barely used in the Greek of his day.
What looks at first like a scattered range of uses is held together by that one idea. Paul can call the whole of salvation a gift of grace, Israel's standing covenant promises a gift of grace, his own rescue from danger a gift of grace, a person's calling to singleness or marriage a gift of grace, and the abilities and roles God hands out in a church a gift of grace. The common thread is never the kind of thing given, but its source and its concreteness: each one is God's grace showing up in a definite form.
The senses below sort those uses by setting, from the largest (salvation itself) down to the everyday gifts at work in a gathered congregation. They are shades of one meaning, not separate words: a reader can use the plain word gift throughout and let the context fill in the rest.
One caution worth flagging up front: the modern word charisma, meaning a magnetic personality, comes from this Greek word but carries almost the opposite weight. That sense was coined much later and reads a star quality into a word that points away from impressive individuals and toward grace freely given to ordinary people.