The phrase "a gesture of their" is correct and usable in written English.
It can be used when referring to an action or expression that signifies goodwill or intention from a group of people.
Example: "The community organized a fundraiser as a gesture of their support for the local hospital."
Alternatives: "a sign of their" or "an expression of their".
They had given their only possession to Maude as a gesture of their gratitude.
The Cubans made a gesture of their own, quietly improving Alan Gross's medical treatment and his living conditions in prison.
Bringing part of this collection back temporarily is a gesture of their understanding how important Butte was in American history.
A Cuban diplomat told me this week, "We've already signalled that we are ready to go ahead with normalization even if we're still officially on the list, but we still need a gesture of their intention to remove us".
She mentions the Phrygian cap, adopted as a symbol by the colonists, who also made homespun cloth to replace fine British textiles, as a gesture of their rejection of British rule.
In 481 BC Xerxes sent ambassadors around Greece asking for earth and water as a gesture of their submission, but making the very deliberate omission of Athens and Sparta (both of whom were at open war with Persia).
Along those lines, a senior aide to Mr. Roh said the president-elect planned to visit United States troops before his inauguration, in a gesture of recognition of their importance for the defense of this country.
Havel, talking to students invited to Hradcany as "a gesture of recognition" of their part in restoring the nation to freedom, told them that while progress had been made in building the political and economic system, too many people thought that "freedom means the right to do anything, or that the market and ethics are mutually exclusive".
"It would be good if there were a gesture of tolerance on their part.
President Vaclav Havel visited the hunger strikers late Friday in a gesture of support for their demands, Czechoslovak televison reported.
